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lattice: clean old classes, add bz_mesh, gf on bz

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This commit is contained in:
Olivier Parcollet 2014-02-16 13:31:27 +01:00
parent e82d95d1a8
commit 6e87bee850
14 changed files with 803 additions and 494 deletions
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32
pytriqs/lattice/lattice_tools.pyx
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@ -10,19 +10,17 @@ from cython.operator cimport dereference as deref, preincrement as inc #derefere
import numpy
cdef extern from "triqs/lattice/bravais_lattice_and_brillouin_zone.hpp" namespace "triqs::gf" :
cdef cppclass bravais_lattice_c " triqs::lattice_tools::bravais_lattice" :
bravais_lattice_c(matrix[double] & units)
cdef extern from "triqs/lattice/brillouin_zone.hpp" :
cdef cppclass bravais_lattice_c " triqs::lattice::bravais_lattice" :
bravais_lattice_c(matrix[double] & units, vector[tqa_vector[double]] &, vector[std_string] &) except +
int n_orbitals()
matrix[double] units()
int dim()
void push_back(std_string &, tqa_vector[double] &)
tqa_vector[double] lattice_to_real_coordinates (tqa_vector_view[double] &)
cdef extern from "triqs/lattice/tight_binding.hpp" namespace "triqs::gf" :
cdef cppclass tight_binding " triqs::lattice_tools::tight_binding" :
tight_binding(bravais_lattice_c & units)
void push_back (vector[long] &, matrix[double] &)
cdef cppclass tight_binding " triqs::lattice::tight_binding" :
tight_binding(bravais_lattice_c & units, vector[vector[long]] &, vector[matrix[dcomplex]] &) except +
#Fix the name conflict pv wiht a pxd, cf doc....?
array_view[complex,THREE] hopping_stack_c "hopping_stack" (tight_binding & TB, array_view[double,TWO] & k_stack)
@ -37,10 +35,13 @@ cdef class BravaisLattice :
cdef bravais_lattice_c * _c
def __init__(self, units, orbital_positions = None ) :
""" """
self._c = new bravais_lattice_c( matrix[double](units))
cdef vector[std_string] names
cdef vector[tqa_vector[double]] atom_pos
orbital_positions = orbital_positions if orbital_positions else dict ("", (0,0,0) )
for name, pos in orbital_positions.items():
self._c.push_back( name, tqa_vector[double](pos))
names.push_back(name)
atom_pos.push_back(tqa_vector[double](pos))
self._c = new bravais_lattice_c( matrix[double](units),atom_pos, names)
def __dealloc__(self):
del self._c
@ -69,11 +70,16 @@ cdef class TightBinding:
cdef tight_binding * _c
def __init__(self, BravaisLattice bravais_lattice, hopping ) :
""" """
self._c = new tight_binding(deref(bravais_lattice._c))
cdef vector[long] d
#self._c = new tight_binding(deref(bravais_lattice._c))
#cdef vector[long] d
cdef vector[matrix[dcomplex]] mats
cdef vector[vector[long]] displs
for displ, mat in hopping.items() :
d = displ
self._c.push_back( d, matrix[double] (numpy.array(mat, dtype =float)))
displs.push_back(displ)
#d = displ
mats.push_back(matrix[dcomplex] (numpy.array(mat, dtype =float)))
#self._c.push_back( d, matrix[double] (numpy.array(mat, dtype =float)))
self._c = new tight_binding(deref(bravais_lattice._c), displs, mats)
def __dealloc__(self):
del self._c

36
test/triqs/gfs/g_k_om.cpp Normal file
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@ -0,0 +1,36 @@
#define TRIQS_ARRAYS_ENFORCE_BOUNDCHECK
#include <triqs/gfs.hpp>
#include <triqs/gfs/bz.hpp>
using namespace triqs::gfs;
using namespace triqs::clef;
using namespace triqs::arrays;
using namespace triqs::lattice;
#define TEST(X) std::cout << BOOST_PP_STRINGIZE((X)) << " ---> " << (X) << std::endl << std::endl;
int main() {
try {
double beta = 1;
auto bz_ = brillouin_zone{bravais_lattice{make_unit_matrix<double>(2)}};
auto g_eps = gf<bz>{{bz_, 1000}, {1, 1}};
auto G = gf<cartesian_product<bz, imfreq>>{{{bz_, 100}, {beta, Fermion, 100}}, {1, 1}};
// try to assign to expression
placeholder<0> k_;
placeholder<1> w_;
auto eps = make_expr( [](k_t const& k) { return -2 * (cos(k(0)) + cos(k(1))); }) ;
G(k_, w_) << 1 / (w_ - eps(k_) - 1 / (w_ + 2));
// hdf5
H5::H5File file("ess_g_k_om.h5", H5F_ACC_TRUNC );
h5_write(file, "g", G);
}
TRIQS_CATCH_AND_ABORT;
}

75
triqs/gfs/bz.hpp Normal file
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@ -0,0 +1,75 @@
/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
*
* Copyright (C) 2012-2013 by O. Parcollet
*
* TRIQS is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#pragma once
#include "./tools.hpp"
#include "./gf.hpp"
#include "./local/tail.hpp"
#include "./domains/R.hpp"
#include "../lattice/bz_mesh.hpp"
#include "./evaluators.hpp"
namespace triqs {
namespace gfs {
struct bz {};
template <typename Opt> struct gf_mesh<bz, Opt> : lattice::bz_mesh {
template <typename... T> gf_mesh(T &&... x) : lattice::bz_mesh(std::forward<T>(x)...) {}
};
namespace gfs_implementation {
// h5 name
template <typename Opt> struct h5_name<bz, matrix_valued, Opt> {
static std::string invoke() { return "BZ"; }
};
/// --------------------------- data access ---------------------------------
template <typename Opt> struct data_proxy<bz, matrix_valued, Opt> : data_proxy_array<std::complex<double>, 3> {};
template <typename Opt> struct data_proxy<bz, scalar_valued, Opt> : data_proxy_array<std::complex<double>, 1> {};
/// --------------------------- evaluator ---------------------------------
// simple evaluation : take the point on the grid...
template <> struct evaluator_fnt_on_mesh<bz> {
lattice::k_t k;
evaluator_fnt_on_mesh() = default;
template <typename MeshType> evaluator_fnt_on_mesh(MeshType const &m, lattice::k_t const &k_) { k = k_; }
template <typename F> auto operator()(F const &f) const DECL_AND_RETURN(f(k));
};
// ------------- evaluator -------------------
// handle the case where the matsu. freq is out of grid...
template <typename Target, typename Opt> struct evaluator<bz, Target, Opt> {
static constexpr int arity = 1;
template <typename G>
std::c14::conditional_t<std::is_same<Target, matrix_valued>::value, arrays::matrix_const_view<std::complex<double>>,
std::complex<double>>
operator()(G const *g, lattice::k_t const &k) const {
auto n = g->mesh().locate_neighbours(k); // TO BE IMPROVED
return (*g)[n];
}
};
}
}
}

82
triqs/lattice/bravais_lattice.hpp Normal file
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@ -0,0 +1,82 @@
/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
*
* Copyright (C) 2011-2014 by M. Ferrero, O. Parcollet
*
* TRIQS is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#pragma once
#include <triqs/arrays.hpp>
#include <string>
#include <vector>
namespace triqs {
namespace lattice {
using r_t = arrays::vector<double>;
using k_t = arrays::vector<double>;
using dcomplex = std::complex<double>;
using arrays::matrix;
using arrays::array;
using arrays::range;
// --------------------------------------------------------
class bravais_lattice {
public:
using point_t = std::vector<int>; // domain concept. PUT on STACK
bravais_lattice(matrix<double> const& units, std::vector<r_t> atom_orb_pos, std::vector<std::string> atom_orb_name);
bravais_lattice(matrix<double> const& units, std::vector<r_t> atom_orb_pos)
: bravais_lattice(units, atom_orb_pos, std::vector<std::string>(atom_orb_pos.size(), "")) {}
bravais_lattice(matrix<double> const& units) : bravais_lattice(units, std::vector<r_t>{{0, 0, 0}}) {}
bravais_lattice() : bravais_lattice(arrays::make_unit_matrix<double>(3)) {}
int n_orbitals() const { return atom_orb_name.size(); }
arrays::matrix_const_view<double> units() const { return units_; }
int dim() const { return dim_; }
/// Transform into real coordinates.
template <typename R> r_t lattice_to_real_coordinates(R const& x) const {
r_t res(3);
res() = 0;
for (int i = 0; i < dim_; i++) res += x(i) * units_(i, range{});
return res;
}
/// Write into HDF5
friend void h5_write(h5::group fg, std::string subgroup_name, bravais_lattice const& bl);
/// Read from HDF5
friend void h5_read(h5::group fg, std::string subgroup_name, bravais_lattice& bl);
// BOOST Serialization
friend class boost::serialization::access;
template <class Archive> void serialize(Archive& ar, const unsigned int version) {
ar& boost::serialization::make_nvp("units", units_);
ar& boost::serialization::make_nvp("atom_orb_pos", atom_orb_pos);
ar& boost::serialization::make_nvp("atom_orb_name", atom_orb_name);
}
private:
matrix<double> units_;
std::vector<r_t> atom_orb_pos; // atom_orb_pos[i] = position of ith atoms/orbitals in the unit cell
std::vector<std::string> atom_orb_name; // names of these atoms/orbitals.
int dim_;
};
}
}

133
triqs/lattice/bravais_lattice_and_brillouin_zone.cpp
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@ -18,79 +18,106 @@
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#include "bravais_lattice_and_brillouin_zone.hpp"
#include "./bravais_lattice.hpp"
#include "./brillouin_zone.hpp"
#include <triqs/arrays/blas_lapack/dot.hpp>
#include <triqs/arrays/linalg/det_and_inverse.hpp>
#include <triqs/arrays/linalg/cross_product.hpp>
namespace triqs { namespace lattice_tools {
namespace triqs {
namespace lattice {
using namespace tqa;
using namespace std;
//using triqs::arrays::blas::dot;
const double almost_zero(1E-10);
const double almost_zero = 1e-10;
bravais_lattice::bravais_lattice( units_type const & units__) : units_(3,3), dim_(units__.shape(0)) {
units_(range(0,dim_),range()) = units__();
units_(range(dim_,3),range()) = 0;
bravais_lattice::bravais_lattice(matrix<double> const& units__, std::vector<r_t> atom_orb_pos_,
std::vector<std::string> atom_orb_name_)
: units_(3, 3), atom_orb_pos(atom_orb_pos_), atom_orb_name(atom_orb_name_) {
dim_ = first_dim(units__);
if ((dim_ < 1) || (dim_ > 3)) TRIQS_RUNTIME_ERROR << " units matrix must be square matrix of size 1, 2 or 3";
using arrays::range;
auto r = range(0, dim_);
units_() = 0;
units_(r, r) = units__(r, r);
// First complete the basis. Add some tests for safety
tqa::vector<double> ux(3),uy(3),uz(3);
assert(dim_==2);
arrays::vector<double> ux(3), uy(3), uz(3);
double delta;
auto _ = range{};
switch (dim_) {
case 1:
ux = units_(0,range());
uz() = 0; uz(1) = 1 ;
uz = uz - dot(uz,ux)* ux;
ux = units_(0, _);
uz() = 0;
uz(1) = 1;
uz = uz - dot(uz, ux) * ux;
// no luck, ux was parallel to z, another one must work
if (sqrt(dot(uz,uz))<almost_zero) {
uz() = 0; uz(2) = 1; // 0,0,1;
uz = uz - dot(uz,ux)* ux;
if (sqrt(dot(uz, uz)) < almost_zero) {
uz() = 0;
uz(2) = 1; // 0,0,1;
uz = uz - dot(uz, ux) * ux;
}
uz /= sqrt(dot(uz,uz));
uy = cross_product(uz,ux);
uy = uy/sqrt(dot(uy,uy)); // uy can not be 0
units_(1,range()) = uz;
units_(2,range()) = uy;
uz /= sqrt(dot(uz, uz));
uy = cross_product(uz, ux);
uy = uy / sqrt(dot(uy, uy)); // uy can not be 0
units_(1, _) = uz;
units_(2, _) = uy;
break;
case 2:
uy() = 0; uy(2) = 1 ;
uy = cross_product(units_(0,range()),units_(1,range()));
double delta = sqrt(dot(uy,uy));
if (abs(delta)<almost_zero) TRIQS_RUNTIME_ERROR<<"Tiling : the 2 vectors of unit are not independent";
units_(2,range()) = uy /delta;
uy() = 0;
uy(2) = 1;
uy = cross_product(units_(0, _), units_(1, _));
delta = sqrt(dot(uy, uy));
if (abs(delta) < almost_zero) TRIQS_RUNTIME_ERROR << "Bravais Lattice : the 2 vectors of unit are not independent : " << units__;
units_(2, _) = uy / delta;
break;
case 3:
TRIQS_RUNTIME_ERROR << " 3d bravais lattice not implemented";
break;
}
//cerr<<" Units = "<< units_<<endl;
}
//------------------------------------------------------------------------------------
/// Write into HDF5
void h5_write(h5::group fg, std::string subgroup_name, bravais_lattice const& bl) {
h5::group gr = fg.create_group(subgroup_name);
h5_write(gr, "units", bl.units_); // NOT COMPLETE
}
/// Read from HDF5
void h5_read(h5::group fg, std::string subgroup_name, bravais_lattice& bl) {
h5::group gr = fg.open_group(subgroup_name);
matrix<double> u;
h5_read(gr, "units", u);
bl = bravais_lattice{u}; // NOT COMPLETE
}
//------------------------------------------------------------------------------------
//------------------------------------------------------------------------------------
brillouin_zone::brillouin_zone( bravais_lattice const & bl_) : lattice_(bl_), K_reciprocal(3,3) {
bravais_lattice::units_type Units(lattice().units());
std::cout << Units << std::endl;
double delta = dot(Units(0,range()), cross_product(Units(1,range()),Units(2,range())));
std::cout << dot(Units(0,range()), cross_product(Units(1,range()),Units(2,range())))<<std::endl;
std::cout << cross_product(Units(1,range()),Units(2,range()))<<std::endl;
if (abs(delta)<almost_zero) TRIQS_RUNTIME_ERROR<<"Tiling : the 3 vectors of Units are not independant";
K_reciprocal(0,range()) = cross_product(Units(1,range()),Units(2,range())) / delta;
K_reciprocal(1,range()) = cross_product(Units(2,range()),Units(0,range())) / delta;
K_reciprocal(2,range()) = cross_product(Units(0,range()),Units(1,range())) / delta;
//for (size_t i =0; i< lattice().dim();i++) std::cerr << " K_reciprocal(" << i << ")/(2pi) = " << K_reciprocal(i,range())<< std::endl;
const double pi = acos(-1.0);
K_reciprocal = K_reciprocal*2*pi;
K_reciprocal_inv = inverse(K_reciprocal);
brillouin_zone::brillouin_zone(bravais_lattice const& bl_) : lattice_(bl_), K_reciprocal(3, 3) {
using arrays::range;
auto _ = range{};
auto Units = lattice().units();
double delta = dot(Units(0, _), cross_product(Units(1, _), Units(2, _)));
if (abs(delta) < almost_zero) TRIQS_RUNTIME_ERROR << "Brillouin Zone : the 3 vectors of Units are not independant" << Units;
K_reciprocal(0, _) = cross_product(Units(1, _), Units(2, _)) / delta;
K_reciprocal(1, _) = cross_product(Units(2, _), Units(0, _)) / delta;
K_reciprocal(2, _) = cross_product(Units(0, _), Units(1, _)) / delta;
K_reciprocal = K_reciprocal * 2 * M_PI;
K_reciprocal_inv = inverse(K_reciprocal);
}
K_view_type brillouin_zone::lattice_to_real_coordinates (K_view_type const & k) const {
if (k.size()!=lattice().dim()) TRIQS_RUNTIME_ERROR<<"latt_to_real_k : dimension of k must be "<<lattice().dim();
K_type res(3); res()=0; int dim = lattice().dim();
for (int i =0; i< dim;i++) res += k (i) * K_reciprocal(i,range());
return(res);
//------------------------------------------------------------------------------------
/// Write into HDF5
void h5_write(h5::group fg, std::string subgroup_name, brillouin_zone const& bz) {
h5::group gr = fg.create_group(subgroup_name);
h5_write(gr, "bravais_lattice", bz.lattice_);
}
K_view_type brillouin_zone::real_to_lattice_coordinates (K_view_type const & k) const {
if (k.size()!=lattice().dim()) TRIQS_RUNTIME_ERROR<<"latt_to_real_k : dimension of k must be "<<lattice().dim();
K_type res(3);res()=0; int dim = lattice().dim();
for (int i =0; i< dim;i++) res += k (i) * K_reciprocal_inv(i,range());
return(res);
/// Read from HDF5
void h5_read(h5::group fg, std::string subgroup_name, brillouin_zone& bz) {
h5::group gr = fg.open_group(subgroup_name);
bravais_lattice bl;
h5_read(gr, "bravais_lattice", bl);
bz = brillouin_zone{bl};
}
}}//namespaces
}
} // namespaces

99
triqs/lattice/bravais_lattice_and_brillouin_zone.hpp
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@ -1,99 +0,0 @@
/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
*
* Copyright (C) 2011 by M. Ferrero, O. Parcollet
*
* TRIQS is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#ifndef TRIQS_LATTICE_BRAVAIS_LATTICE_H
#define TRIQS_LATTICE_BRAVAIS_LATTICE_H
#include <triqs/arrays/array.hpp>
#include <triqs/arrays/matrix.hpp>
#include <triqs/arrays/vector.hpp>
#include <triqs/utility/exceptions.hpp>
#include <unordered_map>
#include <map>
#include <string>
#include <unordered_map>
namespace triqs { namespace lattice_tools {
namespace tqa = triqs::arrays;
using tqa::array; using tqa::array_view; using tqa::matrix_view;using tqa::matrix;using tqa::range;
typedef tqa::vector <double> R_type;
typedef tqa::vector <double> K_type;
typedef tqa::vector_view<double> R_view_type;
typedef tqa::vector_view<double> K_view_type;
typedef std::complex<double> dcomplex;
class bravais_lattice {
public :
typedef matrix<double> units_type;
typedef std::unordered_map<std::string, R_type> orbital_type; // name -> position in space
bravais_lattice(units_type const & units);
size_t n_orbitals() const {return orbitals_.size();}
units_type const & units() const { return units_;}
size_t dim() const { return dim_; }
/**
* Push_back mechanism of a pair orbital_name -> position in R^3
* VectorType is anything from which a tqa::vector <double> can be constructed
*/
template<typename VectorType>
void push_back(std::string const & s, VectorType && v) { orbitals_.insert(std::make_pair(s,std::forward<VectorType>(v)));}
/***
* Transform into real coordinates.
* @param[in] x : coordinates in the basis :unit_i arrays::vector or vector_view
* @return Coordinates in R^3 ("real" coordinates)
*/
template<typename R>
R_view_type lattice_to_real_coordinates(R const & x) const {
R_type res(3); res() =0;
for (size_t i =0; i< dim();i++) res += x (i) * units_(i,range());
return(res);
}
protected :
units_type units_;
size_t dim_;
orbital_type orbitals_;
};
class brillouin_zone {
bravais_lattice lattice_;
tqa::matrix<double> K_reciprocal, K_reciprocal_inv;
public :
brillouin_zone( bravais_lattice const & bl_);
bravais_lattice lattice() const { return lattice_;}
/***
* Transform into real coordinates.
* @param[in] k : coordinates in the basis (K_reciprocal_i)
* @return Coordinates in R^3 ("real" coordinates)
*/
K_view_type lattice_to_real_coordinates (K_view_type const & k) const;
/// Inverse of latt_to_real_k
K_view_type real_to_lattice_coordinates (K_view_type const & k) const;
};
}}
#endif

75
triqs/lattice/brillouin_zone.hpp Normal file
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@ -0,0 +1,75 @@
/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
*
* Copyright (C) 2011-2014 by M. Ferrero, O. Parcollet
*
* TRIQS is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#pragma once
#include "./bravais_lattice.hpp"
namespace triqs {
namespace lattice {
class brillouin_zone {
public:
using point_t = k_t; // domain concept
brillouin_zone() { // default construction, 3d cubic lattice
K_reciprocal = arrays::make_unit_matrix<double>(3);
K_reciprocal_inv() = K_reciprocal;
}
/// Construct from a bravais_lattice
brillouin_zone(bravais_lattice const& bl_);
/// Access to the underlying bravais lattice
bravais_lattice lattice() const { return lattice_; }
/// Transform from lattice to real coordinates
template <typename K> k_t lattice_to_real_coordinates(K const& k) const { return _transfo_impl(k, K_reciprocal); }
/// Transform from real to lattice coordinates
template <typename K> k_t real_to_lattice_coordinates(K const& k) const { return _transfo_impl(k, K_reciprocal_inv); }
/// Write into HDF5
friend void h5_write(h5::group fg, std::string subgroup_name, brillouin_zone const& bz);
/// Read from HDF5
friend void h5_read(h5::group fg, std::string subgroup_name, brillouin_zone& bz);
// BOOST Serialization
friend class boost::serialization::access;
template <class Archive> void serialize(Archive& ar, const unsigned int version) {
ar& boost::serialization::make_nvp("bravais_lattice", lattice_);
}
private:
bravais_lattice lattice_;
arrays::matrix<double> K_reciprocal, K_reciprocal_inv;
template <typename K> k_t _transfo_impl(K const& k, arrays::matrix<double> const& K_base) const {
if (first_dim(k) != lattice().dim()) TRIQS_RUNTIME_ERROR << "latt_to_real_k : dimension of k must be " << lattice().dim();
k_t res(3);
res() = 0;
int dim = lattice().dim();
for (int i = 0; i < dim; i++) res += k(i) * K_reciprocal_inv(i, range{});
return res;
}
};
}
}

75
triqs/lattice/bz_mesh.cpp Normal file
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@ -0,0 +1,75 @@
/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
*
* Copyright (C) 2011 by M. Ferrero, O. Parcollet
*
* TRIQS is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#include "./bz_mesh.hpp"
#include "./grid_generator.hpp"
namespace triqs {
namespace lattice {
bz_mesh::bz_mesh(brillouin_zone const &bz, int n_l) : bz(bz) {
// compute the k points
for (auto grid = grid_generator{bz.lattice().dim(), n_l}; grid; ++grid) k_pt_stack.push_back(*grid);
}
// locate the closest point : VERY PRIMITIVE : TO BE IMPROVED (kd-tree ?)
long bz_mesh::locate_neighbours(k_t k) const {
// reduction to the BZ ?
// very slow : improve with a kd-tree ?
double d_min = 100; // > pi
auto sqr = [](double x) { return x * x; };
int pos = 0, pos_min = 0;
for (auto const &p : k_pt_stack) {
int dim = k.size();
double d = 0;
for (int i = 0; i < dim; ++i) d += sqr(k(i) - p(i));
if (d < d_min) {
d_min = d;
pos_min = pos;
}
pos++;
}
return pos;
}
/// Write into HDF5
void h5_write(h5::group fg, std::string subgroup_name, bz_mesh const &m) {
h5::group gr = fg.create_group(subgroup_name);
h5_write(gr, "domain", m.domain());
auto kp = matrix<double>(m.k_pt_stack.size(), 3);
kp() = 0;
for (int i = 0; i < m.k_pt_stack.size(); ++i) kp(i, range{}) = m.k_pt_stack[i];
h5_write(gr, "k_pt_stack", kp);
}
/// Read from HDF5
void h5_read(h5::group fg, std::string subgroup_name, bz_mesh &m) {
h5::group gr = fg.open_group(subgroup_name);
brillouin_zone dom;
h5_read(gr, "domain", dom);
matrix<double> kp;
h5_read(gr, "k_pt_stack", kp);
std::vector<k_t> k_pt_stack;
int s = first_dim(kp);
for (int i = 0; i < s; ++i) k_pt_stack[i] = kp(i, range{});
m = bz_mesh(std::move(dom), k_pt_stack);
}
}
} // namespaces

109
triqs/lattice/bz_mesh.hpp Normal file
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@ -0,0 +1,109 @@
/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
*
* Copyright (C) 2012 by M. Ferrero, O. Parcollet
*
* TRIQS is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#pragma once
#include "./brillouin_zone.hpp"
#include "../gfs/tools.hpp"
#include "../gfs/meshes/mesh_tools.hpp"
namespace triqs {
namespace lattice {
struct bz_mesh {
using domain_t = brillouin_zone;
using index_t = long;
using domain_pt_t = typename domain_t::point_t;
bz_mesh() = default;
bz_mesh(brillouin_zone const &bz, int n_l);
bz_mesh(brillouin_zone const &bz, std::vector<k_t> k_pt_stack) : bz(bz), k_pt_stack(std::move(k_pt_stack)) {}
domain_t const &domain() const { return bz; }
long size() const { return k_pt_stack.size(); }
/// Conversions point <-> index <-> linear_index
domain_pt_t const &index_to_point(index_t i) const { return k_pt_stack[i]; }
long index_to_linear(index_t ind) const { return ind; }
// f (k) -> void where k is a k_t, a point in the BZ
template <typename F> friend void foreach(bz_mesh const &m, F f) {
for (auto const &k : m.k_pt_stack) f(k);
}
// locate the closest point : VERY PRIMITIVE : TO BE IMPROVED (kd-tree ?)
long locate_neighbours(k_t k) const;
/// The wrapper for the mesh point
class mesh_point_t : gfs::tag::mesh_point, public utility::arithmetic_ops_by_cast<mesh_point_t, domain_pt_t> {
bz_mesh const *m;
index_t _index;
public:
mesh_point_t() : m(nullptr) {}
mesh_point_t(bz_mesh const &mesh, index_t const &index_) : m(&mesh), _index(index_) {}
mesh_point_t(bz_mesh const &mesh) : mesh_point_t(mesh, 0) {}
void advance() { ++_index; }
using cast_t = domain_pt_t;
operator cast_t() const { return m->index_to_point(_index); }
long linear_index() const { return _index; }
long index() const { return _index; }
bool at_end() const { return (_index == m->size()); }
void reset() { _index = 0; }
};
/// Accessing a point of the mesh
mesh_point_t operator[](index_t i) const { return mesh_point_t(*this, i); }
/// Iterating on all the points...
using const_iterator = gfs::mesh_pt_generator<bz_mesh>;
const_iterator begin() const { return const_iterator(this); }
const_iterator end() const { return const_iterator(this, true); }
const_iterator cbegin() const { return const_iterator(this); }
const_iterator cend() const { return const_iterator(this, true); }
/// Mesh comparison
bool operator==(bz_mesh const &M) const { return ( (size() == M.size())); }
//bool operator==(bz_mesh const &M) const { return ((bz == M.bz) && (size() == M.size())); }
bool operator!=(bz_mesh const &M) const { return !(operator==(M)); }
/// Write into HDF5
friend void h5_write(h5::group fg, std::string subgroup_name, bz_mesh const &m);
/// Read from HDF5
friend void h5_read(h5::group fg, std::string subgroup_name, bz_mesh &m);
// BOOST Serialization
friend class boost::serialization::access;
template <class Archive> void serialize(Archive &ar, const unsigned int version) {
ar &boost::serialization::make_nvp("domain", bz);
ar &boost::serialization::make_nvp("k_pt_stack", k_pt_stack);
}
friend std::ostream &operator<<(std::ostream &sout, bz_mesh const &m) { return sout << "Mesh over BZ "; }
private:
domain_t bz;
std::vector<k_t> k_pt_stack;
};
}
}

28
triqs/lattice/concepts.rst
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@ -1,28 +0,0 @@
Concept Function
return_type
arg_type
return_type operator()(arg_type const &) const : the evaluation of the function
Concept FunctionOnBravaisLattice
refines Function
bravais_lattice const & lattice() const
Concept ShortRangeFunctionOnBravaisLattice
* refines FunctionOnBravaisLattice
* derived from Tag::ShortRangeFunctionOnBravaisLattice ??
* map_type
* begin, end: iterator -> pair<arg_type, return_type>
Concept FunctionOnBrillouinZone
* refines Function
brillouin_zone const & bz() const

90
triqs/lattice/functors.hpp
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@ -1,90 +0,0 @@
/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
*
* Copyright (C) 2011 by M. Ferrero, O. Parcollet
*
* TRIQS is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#ifndef TRIQS_LATTICE_FUNCTORS_H
#define TRIQS_LATTICE_FUNCTORS_H
namespace triqs { namespace lattice_tools {
const double pi = acos(-1.0);
const std::complex<double> I(0,1);
template<typename F> struct minus_chech_impl {
typedef typename F::arg_type arg_type;
typedef typename F::return_type return_type;
F f;
minus_chech_impl(F const & f_):f(f_){}
brillouin_zone const & bz() const {return f.bz();}
return_type operator()(arg_type const & x) const { return_type res(f(x)); res *=-1; return res;}
};
namespace result_of { template<typename F> struct minus_chech{ typedef minus_chech_impl<F> type;}; }
/**
* Given f of type F which models FunctionOnBravaisLattice, minus_check(f) :
* - returns -f(-args)
* - its type models Function
*
*/
template<typename F> minus_chech_impl<F> minus_chech(F const & f) { return minus_chech_impl<F> (f);}
template<typename F >//, typename Enabler = boost::enable_if< Tag::check<Tag::ShortRangeFunctionOnBravaisLattice, F> > >
class fourier_impl {
F f;
brillouin_zone bz_;
// deduce the return type from decltype(begin()->second)
public:
typedef typename regular_type_if_exists_else_type< decltype(f.begin()->second)>::type return_construct_type;
typedef typename view_type_if_exists_else_type<return_construct_type>::type return_type;
typedef K_view_type arg_type;
fourier_impl (F f_):f(f_), bz_(f_.lattice()), res(f.n_bands(),f.n_bands()) {}
//brillouin_zone const & bz() const { return bz_; }
return_type operator()(K_view_type const & k) {
res()=0;
for (auto const & pdm : f) { res += pdm.second * exp( 2*pi*I* this->dot_product(k,pdm.first)); }
return res;
}
protected:
inline double dot_product(K_view_type const & a, typename F::arg_type const & b) const {
assert(b.size()>= this->bz_.lattice().dim());
double r=0; for (size_t i=0; i< this->bz_.lattice().dim();++i) r += a(i) * b[i];
return r;
}
return_construct_type res;
//typename F::return_construct_type res;
};
/**
* Given f of type F which models ShortRangeFunctionOnBravaisLattice, Fourier(f) returns
* - a type that models FunctionOnBravaisLattice
* - and returns the Fourier transform f(k)
*/
template<typename F> fourier_impl<F> Fourier(F f) { return fourier_impl<F> (f);}
//namespace result_of { template<typename F> struct Fourier { typedef fourier_impl<F> type;}; }
}}
#endif

107
triqs/lattice/grid_generator.hpp
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@ -1,4 +1,3 @@
/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
@ -19,55 +18,77 @@
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#pragma once
#include "./brillouin_zone.hpp"
#ifndef TRIQS_GRID_GENERATOR_H
#define TRIQS_GRID_GENERATOR_H
#include <triqs/arrays/array.hpp>
namespace triqs { namespace lattice_tools {
namespace triqs {
namespace lattice {
/**
* Generate the point in a cuboid as an array<double,1> const &
*/
class grid_generator :
public boost::iterator_facade< grid_generator, K_type const &, boost::forward_traversal_tag, K_type const & > {
friend class boost::iterator_core_access;
size_t dim, nkpts,nx,ny,nz,N_X,N_Y,N_Z,index_;
double step_x, step_y, step_z;
bool at_end;
K_type pt;
void init() {
nx=0; ny=0; nz=0;at_end = false;index_ =0;
N_X = nkpts;
N_Y = (dim>1 ? nkpts : 1);
N_Z = (dim>2 ? nkpts : 1);
step_x = 1.0/double(N_X); step_y = 1.0/double(N_Y); step_z = 1.0/double(N_Z);
pt(0)=step_x/2; pt(1)=step_y/2; pt(2)=step_z/2;
class grid_generator : public boost::iterator_facade<grid_generator, k_t const &, boost::forward_traversal_tag, k_t const &> {
friend class boost::iterator_core_access;
int dim, nkpts, nx, ny, nz, N_X, N_Y, N_Z, index_;
double step_x, step_y, step_z;
bool at_end;
k_t pt;
void init() {
nx = 0;
ny = 0;
nz = 0;
at_end = false;
index_ = 0;
N_X = nkpts;
N_Y = (dim > 1 ? nkpts : 1);
N_Z = (dim > 2 ? nkpts : 1);
step_x = 1.0 / double(N_X);
step_y = 1.0 / double(N_Y);
step_z = 1.0 / double(N_Z);
pt(0) = step_x / 2;
pt(1) = step_y / 2;
pt(2) = step_z / 2;
}
void increment() {
if (nx < N_X - 1) {
++nx;
pt(0) += step_x;
++index_;
return;
}
void increment() {
if (nx<N_X-1) { ++nx; pt(0) += step_x; ++index_; return;}
pt(0) = step_x/2; nx = 0;
if (ny<N_Y-1) { ++ny; pt(1) += step_y; ++index_; return;}
pt(1) = step_y/2; ny = 0;
if (nz<N_Z-1) { ++nz; pt(2) += step_z; ++index_; return;}
at_end = true;
pt(0) = step_x / 2;
nx = 0;
if (ny < N_Y - 1) {
++ny;
pt(1) += step_y;
++index_;
return;
}
pt(1) = step_y / 2;
ny = 0;
if (nz < N_Z - 1) {
++nz;
pt(2) += step_z;
++index_;
return;
}
at_end = true;
}
value_type dereference() const { return pt;}
bool equal(grid_generator const & other) const { return ((other.dim == dim) && (other.index_==index_) && (other.nkpts==nkpts));}
public:
/// dim : dimension, nkpts : number of k point in each dimension
grid_generator(size_t dim_, size_t nkpts_): dim(dim_),nkpts(nkpts_), pt(3) {init();}
grid_generator():dim(3), nkpts(0), pt(3) {init();}
size_t size () const { return (N_X * N_Y * N_Z);}
size_t index() const { return index_;}
operator bool() const { return !(at_end);}
};
}}
#endif
value_type dereference() const { return pt; }
bool equal(grid_generator const &other) const {
return ((other.dim == dim) && (other.index_ == index_) && (other.nkpts == nkpts));
}
public:
/// dim : dimension, nkpts : number of k point in each dimension
grid_generator(int dim_, int nkpts_) : dim(dim_), nkpts(nkpts_), pt(3) { init(); }
grid_generator() : dim(3), nkpts(0), pt(3) { init(); }
int size() const { return (N_X * N_Y * N_Z); }
int index() const { return index_; }
operator bool() const { return !(at_end); }
};
}
}

236
triqs/lattice/tight_binding.cpp
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@ -22,170 +22,186 @@
#include <triqs/arrays/algorithms.hpp>
#include <triqs/arrays/linalg/eigenelements.hpp>
#include "grid_generator.hpp"
#include "functors.hpp"
namespace triqs { namespace lattice_tools {
using namespace std;
using namespace tqa;
namespace triqs {
namespace lattice {
using namespace arrays;
tight_binding::tight_binding(bravais_lattice const& bl, std::vector<std::vector<long>> all_disp,
std::vector<matrix<dcomplex>> all_matrices)
: bl_(bl), all_disp(std::move(all_disp)), all_matrices(std::move(all_matrices)) {
// checking inputs
if (all_disp.size() != all_matrices.size()) TRIQS_RUNTIME_ERROR << " Number of displacements != Number of matrices";
for (int i = 0; i < all_disp.size(); ++i) {
if (all_disp[i].size() != bl_.dim())
TRIQS_RUNTIME_ERROR << "displacement of incorrect size : got " << all_disp[i].size() << "instead of " << bl_.dim();
if (first_dim(all_matrices[i]) != n_bands())
TRIQS_RUNTIME_ERROR << "the first dim matrix is of size " << first_dim(all_matrices[i]) << " instead of " << n_bands();
if (second_dim(all_matrices[i]) != n_bands())
TRIQS_RUNTIME_ERROR << "the second dim matrix is of size " << second_dim(all_matrices[i]) << " instead of " << n_bands();
}
}
//------------------------------------------------------
array_view <dcomplex,3> hopping_stack (tight_binding const & TB, array_view<double,2> const & k_stack) {
auto TK = Fourier(TB);
array<dcomplex,3> res(TB.n_bands(), TB.n_bands(), k_stack.shape(1));
for(size_t i = 0; i<k_stack.shape(1); ++i) res(range(), range(), i) = TK(k_stack(range(),i));
array<dcomplex, 3> hopping_stack(tight_binding const& TB, arrays::array_const_view<double, 2> k_stack) {
auto TK = fourier(TB);
array<dcomplex, 3> res(TB.n_bands(), TB.n_bands(), k_stack.shape(1));
for (int i = 0; i < k_stack.shape(1); ++i) res(range(), range(), i) = TK(k_stack(range(), i));
return res;
}
//------------------------------------------------------
array_view<double,2> energies_on_bz_path(tight_binding const & TB, K_view_type K1, K_view_type K2, size_t n_pts) {
auto TK = Fourier(TB);
const size_t norb=TB.lattice().n_orbitals();
const size_t ndim=TB.lattice().dim();
array<double,2> eval(norb,n_pts);
K_type dk = (K2 - K1)/double(n_pts), k = K1;
for (size_t i =0; i<n_pts; ++i, k += dk) {
eval(range(),i) = linalg::eigenvalues( TK( k (range(0,ndim))), false);
array<double, 2> energies_on_bz_path(tight_binding const& TB, k_t const& K1, k_t const& K2, int n_pts) {
auto TK = fourier(TB);
int norb = TB.lattice().n_orbitals();
int ndim = TB.lattice().dim();
array<double, 2> eval(norb, n_pts);
k_t dk = (K2 - K1) / double(n_pts), k = K1;
for (int i = 0; i < n_pts; ++i, k += dk) {
eval(range(), i) = linalg::eigenvalues(TK(k(range(0, ndim)))(), false);
}
return eval;
}
//------------------------------------------------------
array_view<double,2> energies_on_bz_grid(tight_binding const & TB, size_t n_pts) {
array<double, 2> energies_on_bz_grid(tight_binding const& TB, int n_pts) {
auto TK = Fourier(TB);
const size_t norb=TB.lattice().n_orbitals();
const size_t ndim=TB.lattice().dim();
grid_generator grid(ndim,n_pts);
array<double,2> eval(norb,grid.size());
for (; grid ; ++grid) {
eval(range(),grid.index()) = linalg::eigenvalues( TK( (*grid) (range(0,ndim))), false);
auto TK = fourier(TB);
int norb = TB.lattice().n_orbitals();
int ndim = TB.lattice().dim();
grid_generator grid(ndim, n_pts);
array<double, 2> eval(norb, grid.size());
for (; grid; ++grid) {
eval(range(), grid.index()) = linalg::eigenvalues(TK((*grid)(range(0, ndim)))(), false);
}
return eval;
}
//------------------------------------------------------
std::pair<array<double,1>, array<double,2> > dos(tight_binding const & TB, size_t nkpts, size_t neps) {
std::pair<array<double, 1>, array<double, 2>> dos(tight_binding const& TB, int nkpts, int neps) {
// The Fourier transform of TK
// auto TK = Fourier(TB); // C++0x ....
auto TK = Fourier(TB);
// The fourier transform of TK
auto TK = fourier(TB);
// loop on the BZ
const size_t ndim=TB.lattice().dim();
const size_t norb=TB.lattice().n_orbitals();
grid_generator grid(ndim,nkpts);
array<double,1> tempeval(norb);
array<dcomplex,3> evec(norb,norb,grid.size());
array<double,2> eval(norb,grid.size());
if (norb ==1)
for (; grid ; ++grid) {
double ee = real(TK( (*grid) (range(0,ndim)))(0,0));
eval(0,grid.index()) =ee;
evec(0,0,grid.index()) =1;
int ndim = TB.lattice().dim();
int norb = TB.lattice().n_orbitals();
grid_generator grid(ndim, nkpts);
array<double, 1> tempeval(norb);
array<dcomplex, 3> evec(norb, norb, grid.size());
array<double, 2> eval(norb, grid.size());
if (norb == 1)
for (; grid; ++grid) {
double ee = real(TK((*grid)(range(0, ndim)))(0, 0));
eval(0, grid.index()) = ee;
evec(0, 0, grid.index()) = 1;
}
else
for (; grid ; ++grid) {
//cerr<<" index = "<<grid.index()<<endl;
array_view <double,1> eval_sl = eval(range(),grid.index());
array_view <dcomplex,2> evec_sl = evec(range(),range(),grid.index());
std::tie (eval_sl,evec_sl) = linalg::eigenelements( TK( (*grid) (range(0,ndim)))); //, true);
//cerr<< " point "<< *grid << " value "<< eval_sl<< endl; //" "<< (*grid) (range(0,ndim)) << endl;
for (; grid; ++grid) {
// cerr<<" index = "<<grid.index()<<endl;
array_view<double, 1> eval_sl = eval(range(), grid.index());
array_view<dcomplex, 2> evec_sl = evec(range(), range(), grid.index());
std::tie(eval_sl, evec_sl) = linalg::eigenelements(TK((*grid)(range(0, ndim)))); //, true);
// cerr<< " point "<< *grid << " value "<< eval_sl<< endl; //" "<< (*grid) (range(0,ndim)) << endl;
}
// define the epsilon mesh, etc.
array<double,1> epsilon(neps);
double epsmax = tqa::max_element(eval);
double epsmin = tqa::min_element(eval);
double deps=(epsmax-epsmin)/neps;
//for (size_t i =0; i< neps; ++i) epsilon(i)= epsmin+i/(neps-1.0)*(epsmax-epsmin);
for (size_t i =0; i< neps; ++i) epsilon(i)=epsmin+(i+0.5)*deps;
array<double, 1> epsilon(neps);
double epsmax = max_element(eval);
double epsmin = min_element(eval);
double deps = (epsmax - epsmin) / neps;
// for (int i =0; i< neps; ++i) epsilon(i)= epsmin+i/(neps-1.0)*(epsmax-epsmin);
for (int i = 0; i < neps; ++i) epsilon(i) = epsmin + (i + 0.5) * deps;
// bin the eigenvalues according to their energy
// NOTE: a is defined as an integer. it is the index for the DOS.
//REPORT <<"Starting Binning ...."<<endl;
array<double,2> rho (neps,norb);rho()=0;
for(size_t l=0;l<norb;l++){
for (size_t j=0;j<grid.size();j++){
for (size_t k=0;k<norb;k++){
int a=int((eval(k,j)-epsmin)/deps);
if(a==int(neps)) a=a-1;
rho(a,l) += real(conj(evec(l,k,j))*evec(l,k,j));
//dos(a) += real(conj(evec(l,k,j))*evec(l,k,j));
// REPORT <<"Starting Binning ...."<<endl;
array<double, 2> rho(neps, norb);
rho() = 0;
for (int l = 0; l < norb; l++) {
for (int j = 0; j < grid.size(); j++) {
for (int k = 0; k < norb; k++) {
int a = int((eval(k, j) - epsmin) / deps);
if (a == int(neps)) a = a - 1;
rho(a, l) += real(conj(evec(l, k, j)) * evec(l, k, j));
// dos(a) += real(conj(evec(l,k,j))*evec(l,k,j));
}
}
}
//rho = rho / double(grid.size()*deps);
rho /= grid.size()*deps;
return std::make_pair( epsilon, rho);
// rho = rho / double(grid.size()*deps);
rho /= grid.size() * deps;
return std::make_pair(epsilon, rho);
}
//----------------------------------------------------------------------------------
std::pair<array<double,1>, array<double,1> > dos_patch(tight_binding const & TB, const array<double,2> & triangles, size_t neps, size_t ndiv) {
std::pair<array<double, 1>, array<double, 1>> dos_patch(tight_binding const& TB, const array<double, 2>& triangles, int neps,
int ndiv) {
// WARNING: This version only works for a single band Hamiltonian in 2 dimensions!!!!
// triangles is an array of points defining the triangles of the patch
// neps in the number of bins in energy
// ndiv in the number of divisions used to divide the triangles
//const size_t ndim=TB.lattice().dim();
//const size_t norb=TB.lattice().n_orbitals();
int ntri = triangles.shape(0)/3;
array<double,1> dos(neps);
// int ndim=TB.lattice().dim();
// int norb=TB.lattice().n_orbitals();
int ntri = triangles.shape(0) / 3;
array<double, 1> dos(neps);
// Check consistency
const size_t ndim=TB.lattice().dim();
//const size_t norb=TB.lattice().n_orbitals();
if (ndim !=2) TRIQS_RUNTIME_ERROR<<"dos_patch : dimension 2 only !";
if (triangles.shape(1) != ndim) TRIQS_RUNTIME_ERROR<<"dos_patch : the second dimension of the 'triangle' array in not "<<ndim;
int ndim = TB.lattice().dim();
// int norb=TB.lattice().n_orbitals();
if (ndim != 2) TRIQS_RUNTIME_ERROR << "dos_patch : dimension 2 only !";
if (triangles.shape(1) != ndim)
TRIQS_RUNTIME_ERROR << "dos_patch : the second dimension of the 'triangle' array in not " << ndim;
// Every triangle has ndiv*ndiv k points
size_t nk = ntri*ndiv*ndiv;
size_t k_index = 0;
double epsmax=-100000,epsmin=100000;
array<dcomplex,2> thop(1,1);
array<double,1> energ(nk), weight(nk);
int nk = ntri * ndiv * ndiv;
int k_index = 0;
double epsmax = -100000, epsmin = 100000;
array<dcomplex, 2> thop(1, 1);
array<double, 1> energ(nk), weight(nk);
// a, b, c are the corners of the triangle
// g the center of gravity taken from a
array<double,1> a(ndim), b(ndim), c(ndim), g(ndim), rv(ndim);
array<double, 1> a(ndim), b(ndim), c(ndim), g(ndim), rv(ndim);
int pt = 0;
double s, t;
// The Fourier transform of TK
auto TK = Fourier(TB);
// The fourier transform of TK
auto TK = fourier(TB);
// loop over the triangles
for (int tri = 0; tri < ntri; tri++) {
a = triangles(pt,range());
a = triangles(pt, range());
pt++;
b = triangles(pt,range());
b = triangles(pt, range());
pt++;
c = triangles(pt,range());
c = triangles(pt, range());
pt++;
g = ((a+b+c)/3.0-a)/double(ndiv);
g = ((a + b + c) / 3.0 - a) / double(ndiv);
// the area around a k point might be different from one triangle to the other
// so I use it to weight the sum in the dos
double area = abs(0.5*((b(0)-a(0))*(c(1)-a(1))-(b(1)-a(1))*(c(0)-a(0)))/(ndiv*ndiv));
double area = abs(0.5 * ((b(0) - a(0)) * (c(1) - a(1)) - (b(1) - a(1)) * (c(0) - a(0))) / (ndiv * ndiv));
for (size_t i = 0; i<ndiv; i++) {
s = i/double(ndiv);
for (size_t j = 0; j<ndiv-i; j++) {
t = j/double(ndiv);
for (size_t k = 0; k<2; k++) {
for (int i = 0; i < ndiv; i++) {
s = i / double(ndiv);
for (int j = 0; j < ndiv - i; j++) {
t = j / double(ndiv);
for (int k = 0; k < 2; k++) {
rv = a+s*(b-a)+t*(c-a)+(k+1.0)*g;
rv = a + s * (b - a) + t * (c - a) + (k + 1.0) * g;
if(k==0 || j < ndiv-i-1) {
if (k == 0 || j < ndiv - i - 1) {
energ(k_index) = real(TK(rv)(0,0));
//compute(rv);
//energ(k_index) = real(tk_for_eval(1,1)); //tk_for_eval is Fortran array
energ(k_index) = real(TK(rv)(0, 0));
// compute(rv);
// energ(k_index) = real(tk_for_eval(1,1)); //tk_for_eval is Fortran array
weight(k_index) = area;
if (energ(k_index)>epsmax) epsmax=energ(k_index);
if (energ(k_index)<epsmin) epsmin=energ(k_index);
if (energ(k_index) > epsmax) epsmax = energ(k_index);
if (energ(k_index) < epsmin) epsmin = energ(k_index);
k_index++;
}
}
@ -196,27 +212,23 @@ using namespace std;
assert(k_index == nk);
// define the epsilon mesh, etc.
array<double,1> epsilon(neps);
double deps=(epsmax-epsmin)/neps;
for (size_t i =0; i< neps; ++i) epsilon(i)= epsmin+i/(neps-1.0)*(epsmax-epsmin);
array<double, 1> epsilon(neps);
double deps = (epsmax - epsmin) / neps;
for (int i = 0; i < neps; ++i) epsilon(i) = epsmin + i / (neps - 1.0) * (epsmax - epsmin);
// bin the eigenvalues according to their energy
int ind;
double totalweight(0.0);
dos() = 0.0;
for (size_t j = 0; j < nk; j++) {
ind=int((energ(j)-epsmin)/deps);
for (int j = 0; j < nk; j++) {
ind = int((energ(j) - epsmin) / deps);
if (ind == int(neps)) ind--;
dos(ind) += weight(j);
totalweight += weight(j);
}
dos /= deps;// Normalize the DOS
return std::make_pair(epsilon, dos);
dos /= deps; // Normalize the DOS
return {std::move(epsilon), std::move(dos)};
}
}}
}
}

106
triqs/lattice/tight_binding.hpp
View File

@ -18,74 +18,82 @@
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#ifndef TRIQS_LATTICE_TIGHTBINDINGS_H
#define TRIQS_LATTICE_TIGHTBINDINGS_H
#include "bravais_lattice_and_brillouin_zone.hpp"
#pragma once
#include "brillouin_zone.hpp"
#include <triqs/utility/complex_ops.hpp>
namespace triqs { namespace lattice_tools {
namespace triqs {
namespace lattice {
/**
For tightbinding Hamiltonian with fully localised orbitals
Model the ShortRangeFunctionOnBravaisLattice concept.
Overlap between orbital is taken as unit matrix.
*/
class tight_binding {
typedef std::vector<std::pair<std::vector<long>, matrix<dcomplex>>> displ_value_stack_t;
displ_value_stack_t displ_value_stack;
bravais_lattice bl_;
public :
typedef std::vector<long> arg_type;
///
tight_binding (bravais_lattice const & bl) : bl_(bl) {};
bravais_lattice bl_;
std::vector<std::vector<long>> all_disp;
std::vector<matrix<dcomplex>> all_matrices;
/// Underlying lattice
bravais_lattice const & lattice() const { return bl_;}
public:
///
tight_binding(bravais_lattice const& bl, std::vector<std::vector<long>> all_disp, std::vector<matrix<dcomplex>> all_matrices);
/// Number of bands, i.e. size of the matrix t(k)
size_t n_bands() const { return bl_.n_orbitals();}
/// Underlying lattice
bravais_lattice const& lattice() const { return bl_; }
/**
* Push_back mechanism of a pair displacement -> matrix
* VectorIntType is anything from which a std::vector<long> can be constructed
* MatrixDComplexType is anything from which a matrix<dcomplex> can be constructed
*/
template<typename VectorIntType, typename MatrixDComplexType>
void push_back(VectorIntType && v, MatrixDComplexType && m) {
std::vector<long> V(std::forward<VectorIntType>(v));
if (v.size() != bl_.dim()) TRIQS_RUNTIME_ERROR<<"tight_binding : displacement of incorrect size : got "<< v.size() << "instead of "<< bl_.dim();
matrix<dcomplex> M(std::forward<MatrixDComplexType>(m));
if (first_dim(M) != n_bands()) TRIQS_RUNTIME_ERROR<<"tight_binding : the first dim matrix is of size "<< first_dim(M) <<" instead of "<< n_bands();
if (second_dim(M) != n_bands()) TRIQS_RUNTIME_ERROR<<"tight_binding : the first dim matrix is of size "<< second_dim(M) <<" instead of "<< n_bands();
displ_value_stack.push_back(std::make_pair(std::move(V), std::move(M)));
}
/// Number of bands, i.e. size of the matrix t(k)
int n_bands() const { return bl_.n_orbitals(); }
void reserve(size_t n) { displ_value_stack.reserve(n);}
// calls F(R, t(R)) for all R
template <typename F> friend void foreach(tight_binding const& tb, F f) {
int n = tb.all_disp.size();
for (int i = 0; i < n; ++i) f(tb.all_disp[i], tb.all_matrices[i]);
}
// iterators
typedef displ_value_stack_t::const_iterator const_iterator;
typedef displ_value_stack_t::iterator iterator;
const_iterator begin() const { return displ_value_stack.begin();}
const_iterator end() const { return displ_value_stack.end();}
iterator begin() { return displ_value_stack.begin();}
iterator end() { return displ_value_stack.end();}
};
// a simple function on the domain brillouin_zone
struct fourier_impl {
tight_binding const& tb;
const int nb;
using domain_t = brillouin_zone;
brillouin_zone domain() const {
return {tb.lattice()};
}
template <typename K> matrix<dcomplex> operator()(K const& k) {
matrix<dcomplex> res(nb, nb);
res() = 0;
foreach(tb, [&](std::vector<long> const& displ, matrix<dcomplex> const& m) {
double dot_prod = 0;
int imax = displ.size();
for (int i = 0; i < imax; ++i) dot_prod += k(i) * displ[i];
//double dot_prod = k(0) * displ[0] + k(1) * displ[1];
res += m * exp(2_j * M_PI * dot_prod);
});
return res;
}
};
fourier_impl friend fourier(tight_binding const& tb) {
return {tb, tb.n_bands()};
}
}; // tight_binding
/**
Factorized version of hopping (for speed)
k_in[:,n] is the nth vector
In the result, R[:,:,n] is the corresponding hopping t(k)
*/
array_view <dcomplex,3> hopping_stack (tight_binding const & TB, array_view<double,2> const & k_stack);
array<dcomplex, 3> hopping_stack(tight_binding const& TB, arrays::array_const_view<double, 2> k_stack);
// not optimal ordering here
std::pair<array<double,1>, array<double,2> > dos(tight_binding const & TB, size_t nkpts, size_t neps);
std::pair<array<double,1>, array<double,1> > dos_patch(tight_binding const & TB, const array<double,2> & triangles, size_t neps, size_t ndiv);
array_view<double,2> energies_on_bz_path(tight_binding const & TB, K_view_type K1, K_view_type K2, size_t n_pts);
array_view<double,2> energies_on_bz_grid(tight_binding const & TB, size_t n_pts);
}}
#endif
std::pair<array<double, 1>, array<double, 2>> dos(tight_binding const& TB, int nkpts, int neps);
std::pair<array<double, 1>, array<double, 1>> dos_patch(tight_binding const& TB, const array<double, 2>& triangles, int neps,
int ndiv);
array<double, 2> energies_on_bz_path(tight_binding const& TB, k_t const& K1, k_t const& K2, int n_pts);
array<double, 2> energies_on_bz_grid(tight_binding const& TB, int n_pts);
}
}