mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 19:53:45 +01:00
296 lines
9.6 KiB
Plaintext
296 lines
9.6 KiB
Plaintext
#include "tight_binding.hpp"
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#include <triqs/arrays/expressions/arithmetic.hpp>
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#include <triqs/arrays/expressions/min_max.hpp>
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#include <triqs/arrays/linalg/eigenelements.hpp>
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#include <triqs/python_tools/converters.hpp>
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#include "grid_generator.hpp"
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#include "functors.hpp"
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using namespace std;
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namespace triqs { namespace lattice_tools {
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using namespace tqa;
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tight_binding::tight_binding(bravais_lattice const & bl__, map_type const & t_r) : bl_(bl__),tr(t_r) {check();}
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tight_binding::tight_binding(bravais_lattice const & bl__,boost::python::object dct) :
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bl_(bl__), tr(triqs::python_tools::Py_to_C::convert<map_type>::invoke(dct)) {check();}
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void tight_binding::check() {
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const size_t no = bl_.n_orbitals();
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for (map_type::const_iterator it = tr.begin(); it !=tr.end(); ++it) {
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if (it->second.len(0) != no) throw triqs::runtime_error()<<"tight_binding construction : the first dim matrix is of size "<< it->second.len(0) <<" instead of "<< no;
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if (it->second.len(1) != no) throw triqs::runtime_error()<<"tight_binding construction : the second dim matrix is of size "<< it->second.len(1) <<" instead of "<< no;
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}
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}
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//------------------------------------------------------
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array_view <dcomplex,3> hopping_stack (tight_binding const & TB, array<double,2> const & k_stack) {
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result_of::Fourier<tight_binding>::type TK = Fourier(TB);
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array<dcomplex,3> res(TB.n_bands(), TB.n_bands(), k_stack.len(1));
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for(size_t i = 0; i<k_stack.len(1); ++i) res(range(), range(), i) = TK(k_stack(range(),i));
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return res;
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}
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//------------------------------------------------------
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array_view<double,2> energies_on_bz_path(tight_binding const & TB, K_view_type K1, K_view_type K2, size_t n_pts) {
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result_of::Fourier<tight_binding>::type TK = Fourier(TB);
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const size_t norb=TB.lattice().n_orbitals();
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const size_t ndim=TB.lattice().dim();
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array<double,2> eval(norb,n_pts);
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K_type dk = (K2 - K1)/double(n_pts), k = K1;
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for (size_t i =0; i<n_pts; ++i, k += dk) {
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eval(range(),i) = linalg::eigenvalues( TK( k (range(0,ndim))), false);
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}
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return eval;
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}
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//------------------------------------------------------
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array_view<double,2> energies_on_bz_grid(tight_binding const & TB, size_t n_pts) {
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result_of::Fourier<tight_binding>::type TK = Fourier(TB);
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const size_t norb=TB.lattice().n_orbitals();
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const size_t ndim=TB.lattice().dim();
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grid_generator grid(ndim,n_pts);
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array<double,2> eval(norb,grid.size());
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for (; grid ; ++grid) {
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eval(range(),grid.index()) = linalg::eigenvalues( TK( (*grid) (range(0,ndim))), false);
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}
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return eval;
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}
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//------------------------------------------------------
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struct bz_grid {
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const brillouin_zone bz;
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const size_t nkpts, dim;
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const size_t N_Z,N_Y,N_X;
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size_t size () const { return (N_X * N_Y * N_Z);}
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bz_grid( brillouin_zone const & bz_, size_t nkpts_) :
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bz(bz_),
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nkpts(nkpts_), dim (bz.lattice().dim()),
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N_X (nkpts), N_Y (dim>1 ? nkpts : 1), N_Z (dim>2 ? nkpts : 1) {}
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template <class F>
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void foreach(F f) {
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K_type k(3);
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for (int nz = 0; nz < N_Z; nz++)
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for (int ny = 0; ny < N_Y; ny++)
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for (int nx = 0; nx < N_X; nx++) {
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k(0) = nx/double(N_X);
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k(1) = ny/double(N_Y);
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k(2) = nz/double(N_Z);
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f(k);
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}
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}
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};
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#ifndef TRIQS_HAS_CPP11_LAMBDA
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void lambda_loop( result_of::Fourier<tight_binding>::type const & TK,
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array<dcomplex,3> & evec, array<double,2> & eval,
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size_t & index, size_t ndim, K_type const & k) {
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array_view <double,1> eval_sl = eval(range(),index);
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array_view <dcomplex,2> evec_sl = evec(range(),range(),index);
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boost::tie (eval_sl,evec_sl) = linalg::eigenelements( TK( k(range(0,ndim)))) ;//, true);
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index++;
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}
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}}
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#include <boost/lambda/bind.hpp>
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#include <boost/ref.hpp>
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namespace triqs { namespace lattice_tools {
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namespace BLL=boost::lambda;
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using boost::ref;
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using boost::cref;
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#endif
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std::pair<array<double,1>, array<double,2> > dos(tight_binding const & TB, size_t nkpts, size_t neps) {
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// The Fourier transform of TK
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// auto TK = Fourier(TB); // C++0x ....
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result_of::Fourier<tight_binding>::type TK = Fourier(TB);
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// loop on the BZ
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const size_t ndim=TB.lattice().dim();
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const size_t norb=TB.lattice().n_orbitals();
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bz_grid grid(brillouin_zone(TB.lattice()),nkpts);
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//grid_generator grid(ndim,nkpts);
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array<double,1> tempeval(norb);
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array<dcomplex,3> evec(norb,norb,grid.size());
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array<double,2> eval(norb,grid.size());
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size_t index=0;
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#ifdef TRIQS_HAS_CPP11_LAMBDA
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grid.foreach([&] {
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array_view <double,1> eval_sl = eval(range(),index);
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array_view <dcomplex,2> evec_sl = evec(range(),range(),index);
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boost::tie (eval_sl,evec_sl) = linalg::eigenelements( TK( k(range(0,ndim))), true);
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index++;
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});
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#else
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int N_X (nkpts), N_Y (ndim>1 ? nkpts : 1), N_Z (ndim>2 ? nkpts : 1);
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K_type k(3);
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for (int nz = 0; nz < N_Z; nz++)
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for (int ny = 0; ny < N_Y; ny++)
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for (int nx = 0; nx < N_X; nx++) {
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k(0) = nx/double(N_X);
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k(1) = ny/double(N_Y);
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k(2) = nz/double(N_Z);
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array_view <double,1> eval_sl = eval(range(),index);
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array_view <dcomplex,2> evec_sl = evec(range(),range(),index);
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boost::tie (eval_sl,evec_sl) = linalg::eigenelements( TK( k(range(0,ndim)))) ;//, true);
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index++;
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}
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// grid.foreach(BLL::bind(lambda_loop,cref(TK),ref(evec),ref(eval),ref(index),ndim,BLL::_1));
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#endif
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/*
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for (; grid ; ++grid) {
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//cerr<<" index = "<<grid.index()<<endl;
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array_view <double,1> eval_sl = eval(range(),grid.index());
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array_view <dcomplex,2> evec_sl = evec(range(),range(),grid.index());
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boost::tie (eval_sl,evec_sl) = linalg::eigenelements( TK( (*grid) (range(0,ndim))), true);
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//cerr<< " point "<< *grid << " value "<< eval_sl<< endl; //" "<< (*grid) (range(0,ndim)) << endl;
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}
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*/
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// define the epsilon mesh, etc.
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array<double,1> epsilon(neps);
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double epsmax = tqa::max_element(eval);
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double epsmin = tqa::min_element(eval);
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double deps=(epsmax-epsmin)/neps;
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//for (size_t i =0; i< neps; ++i) epsilon(i)= epsmin+i/(neps-1.0)*(epsmax-epsmin);
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for (size_t i =0; i< neps; ++i) epsilon(i)=epsmin+(i+0.5)*deps;
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// bin the eigenvalues according to their energy
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// NOTE: a is defined as an integer. it is the index for the DOS.
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//REPORT <<"Starting Binning ...."<<endl;
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array<double,2> rho (neps,norb);rho()=0;
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for(size_t l=0;l<norb;l++){
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for (size_t j=0;j<grid.size();j++){
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for (size_t k=0;k<norb;k++){
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int a=int((eval(k,j)-epsmin)/deps);
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if(a==int(neps)) a=a-1;
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rho(l,a) += real(conj(evec(l,k,j))*evec(l,k,j));
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//dos(a) += real(conj(evec(l,k,j))*evec(l,k,j));
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}
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}
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}
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//rho = rho / double(grid.size()*deps);
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rho /= grid.size()*deps;
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return std::make_pair( epsilon, rho);
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}
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//----------------------------------------------------------------------------------
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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) {
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// WARNING: This version only works for a single band Hamiltonian in 2 dimensions!!!!
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// triangles is an array of points defining the triangles of the patch
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// neps in the number of bins in energy
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// ndiv in the number of divisions used to divide the triangles
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//const size_t ndim=TB.lattice().dim();
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//const size_t norb=TB.lattice().n_orbitals();
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int ntri = triangles.len(0)/3;
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array<double,1> dos(neps);
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// Check consistency
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const size_t ndim=TB.lattice().dim();
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//const size_t norb=TB.lattice().n_orbitals();
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if (ndim !=2) throw triqs::runtime_error()<<"dos_patch : dimension 2 only !";
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if (triangles.len(1) != ndim) throw triqs::runtime_error()<<"dos_patch : the second dimension of the 'triangle' array in not "<<ndim;
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// Every triangle has ndiv*ndiv k points
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size_t nk = ntri*ndiv*ndiv;
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size_t k_index = 0;
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double epsmax=-100000,epsmin=100000;
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array<dcomplex,2> thop(1,1);
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array<double,1> energ(nk), weight(nk);
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// a, b, c are the corners of the triangle
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// g the center of gravity taken from a
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array<double,1> a(ndim), b(ndim), c(ndim), g(ndim), rv(ndim);
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int pt = 0;
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double s, t;
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// The Fourier transform of TK
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// auto TK = Fourier(TB); // C++0x ....
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result_of::Fourier<tight_binding>::type TK = Fourier(TB);
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// loop over the triangles
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for (int tri = 0; tri < ntri; tri++) {
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a = triangles(pt,range());
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pt++;
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b = triangles(pt,range());
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pt++;
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c = triangles(pt,range());
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pt++;
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g = ((a+b+c)/3.0-a)/double(ndiv);
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// the area around a k point might be different from one triangle to the other
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// so I use it to weight the sum in the dos
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double area = abs(0.5*((b(0)-a(0))*(c(1)-a(1))-(b(1)-a(1))*(c(0)-a(0)))/(ndiv*ndiv));
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for (size_t i = 0; i<ndiv; i++) {
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s = i/double(ndiv);
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for (size_t j = 0; j<ndiv-i; j++) {
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t = j/double(ndiv);
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for (size_t k = 0; k<2; k++) {
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rv = a+s*(b-a)+t*(c-a)+(k+1.0)*g;
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if(k==0 || j < ndiv-i-1) {
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energ(k_index) = real(TK(rv)(0,0));
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//compute(rv);
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//energ(k_index) = real(tk_for_eval(1,1)); //tk_for_eval is Fortran array
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weight(k_index) = area;
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if (energ(k_index)>epsmax) epsmax=energ(k_index);
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if (energ(k_index)<epsmin) epsmin=energ(k_index);
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k_index++;
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}
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}
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}
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}
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}
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// check consistency
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assert(k_index == nk);
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// define the epsilon mesh, etc.
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array<double,1> epsilon(neps);
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double deps=(epsmax-epsmin)/neps;
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for (size_t i =0; i< neps; ++i) epsilon(i)= epsmin+i/(neps-1.0)*(epsmax-epsmin);
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// bin the eigenvalues according to their energy
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int ind;
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double totalweight(0.0);
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dos() = 0.0;
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for (size_t j = 0; j < nk; j++) {
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ind=int((energ(j)-epsmin)/deps);
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if (ind == int(neps)) ind--;
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dos(ind) += weight(j);
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totalweight += weight(j);
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}
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dos /= deps;// Normalize the DOS
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return std::make_pair(epsilon, dos);
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}
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}}
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