mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 11:43:47 +01:00
346 lines
12 KiB
C++
346 lines
12 KiB
C++
/*******************************************************************************
|
|
*
|
|
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
|
|
*
|
|
* Copyright (C) 2014 by I. Krivenko, O. Parcollet, M. Ferrero
|
|
*
|
|
* 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/utility/dressed_iterator.hpp>
|
|
|
|
#include <ostream>
|
|
#include <limits>
|
|
#include <cmath>
|
|
#include <complex>
|
|
#include <boost/variant.hpp>
|
|
#include <boost/operators.hpp>
|
|
#include <boost/serialization/vector.hpp>
|
|
#include <boost/serialization/map.hpp>
|
|
#include <boost/serialization/variant.hpp>
|
|
|
|
namespace triqs {
|
|
namespace utility {
|
|
|
|
/**
|
|
* many_body_operator is a general operator in second quantification
|
|
*/
|
|
template <typename scalar_t>
|
|
class many_body_operator :
|
|
// implements vector space over scalar_t operators
|
|
boost::additive<many_body_operator<scalar_t>>,
|
|
boost::multipliable<many_body_operator<scalar_t>>,
|
|
boost::additive<many_body_operator<scalar_t>, scalar_t>, // op+a a+op op-a
|
|
//boost::subtractable2_left<many_body_operator<scalar_t>, scalar_t>, // a-op
|
|
boost::multipliable<many_body_operator<scalar_t>, scalar_t>, // op*a a*op op/a
|
|
boost::dividable<many_body_operator<scalar_t>, scalar_t> {
|
|
|
|
static constexpr scalar_t threshold = std::numeric_limits<scalar_t>::epsilon();
|
|
|
|
public:
|
|
/// The indices of the C, C^+ operators are a vector of int/string
|
|
using indices_t = std::vector<boost::variant<int, std::string>>;
|
|
|
|
private:
|
|
// The canonical operator: a dagger and some indices
|
|
struct canonical_ops_t {
|
|
bool dagger;
|
|
indices_t indices;
|
|
// Order: dagger < non dagger, and then indices
|
|
// Example: c+_1 < c+_2 < c+_3 < c_3 < c_2 < c_1
|
|
friend bool operator<(canonical_ops_t const& a, canonical_ops_t const& b) {
|
|
if (a.dagger != b.dagger) return (a.dagger > b.dagger);
|
|
if (a.dagger) // a.indices < b.indices
|
|
return std::lexicographical_compare(a.indices.begin(), a.indices.end(), b.indices.begin(), b.indices.end());
|
|
else // b.indices < a.indices
|
|
return std::lexicographical_compare(b.indices.begin(), b.indices.end(), a.indices.begin(), a.indices.end());
|
|
}
|
|
friend bool operator>(canonical_ops_t const& a, canonical_ops_t const& b) { return b < a; }
|
|
friend bool operator==(canonical_ops_t const& a, canonical_ops_t const& b) {
|
|
return (a.dagger == b.dagger && a.indices.size() == b.indices.size() &&
|
|
std::equal(a.indices.begin(), a.indices.end(), b.indices.begin()));
|
|
}
|
|
template <class Archive> void serialize(Archive& ar, const unsigned int version) { ar& dagger& indices; }
|
|
};
|
|
|
|
// Monomial: an ordered set of creation/annihilation operators and comparison
|
|
using monomial_t = std::vector<canonical_ops_t>;
|
|
|
|
friend bool operator<(monomial_t const& m1, monomial_t const& m2) {
|
|
return m1.size() != m2.size() ? m1.size() < m2.size()
|
|
: std::lexicographical_compare(m1.begin(), m1.end(), m2.begin(), m2.end());
|
|
}
|
|
|
|
// Map of all monomials with coefficients
|
|
using monomials_map_t = std::map<monomial_t, scalar_t>;
|
|
|
|
monomials_map_t monomials;
|
|
|
|
public:
|
|
many_body_operator() = default;
|
|
many_body_operator(many_body_operator const&) = default;
|
|
many_body_operator(many_body_operator&&) = default;
|
|
many_body_operator& operator=(many_body_operator const&) = default;
|
|
many_body_operator& operator=(many_body_operator&&) = default;
|
|
|
|
template <typename S> many_body_operator(many_body_operator<S> const& x) { *this = x; }
|
|
|
|
template <typename S> many_body_operator& operator=(many_body_operator<S> const& x) {
|
|
monomials.clear();
|
|
for (auto const& y : x.monomials) monomials.insert({y.first, y.second});
|
|
}
|
|
|
|
// factory for c, cdag
|
|
static many_body_operator make_canonical(bool is_dag, indices_t indices) {
|
|
many_body_operator res;
|
|
auto m = monomial_t{canonical_ops_t{is_dag, indices}};
|
|
res.monomials.insert({m, 1.0});
|
|
return res;
|
|
}
|
|
|
|
// We use utility::dressed_iterator to dress iterators
|
|
// _cdress is a simple struct of refs to dress the iterators (Cf doc)
|
|
struct _cdress {
|
|
monomial_t const& monomial;
|
|
scalar_t coef;
|
|
_cdress(typename monomials_map_t::const_iterator _it) : monomial(_it->first), coef(_it->second) {}
|
|
};
|
|
using const_iterator = utility::dressed_iterator<typename monomials_map_t::const_iterator, _cdress>;
|
|
|
|
public:
|
|
// Iterators (only const!)
|
|
const_iterator begin() const noexcept { return monomials.begin(); }
|
|
const_iterator end() const noexcept { return monomials.end(); }
|
|
const_iterator cbegin() const noexcept { return monomials.cbegin(); }
|
|
const_iterator cend() const noexcept { return monomials.cend(); }
|
|
|
|
// Is zero operator ?
|
|
bool is_zero() const { return monomials.empty(); }
|
|
|
|
// Algebraic operations involving scalar_t constants
|
|
many_body_operator operator-() const {
|
|
auto res = *this;
|
|
for (auto& m : res.monomials) m.second = -m.second;
|
|
return res;
|
|
}
|
|
|
|
many_body_operator& operator+=(scalar_t alpha) {
|
|
bool is_new_monomial;
|
|
typename monomials_map_t::iterator it;
|
|
std::tie(it, is_new_monomial) = monomials.insert(std::make_pair(monomial_t(0), alpha));
|
|
if (!is_new_monomial) {
|
|
it->second += alpha;
|
|
erase_zero_monomial(monomials, it);
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
many_body_operator& operator-=(scalar_t alpha) { return operator+=(-alpha); }
|
|
|
|
friend many_body_operator operator-(scalar_t alpha, many_body_operator const& op) { return -op + alpha; }
|
|
//friend many_body_operator operator/ (many_body_operator const & op, scalar_t alpha) { return op/alpha; }
|
|
|
|
many_body_operator& operator*=(scalar_t alpha) {
|
|
if (std::abs(alpha) < 100*std::abs(threshold)) {
|
|
monomials.clear();
|
|
} else {
|
|
for (auto& m : monomials) m.second *= alpha;
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
many_body_operator& operator/=(scalar_t alpha) { return operator*=(1.0/alpha); }
|
|
|
|
// Algebraic operations
|
|
many_body_operator& operator+=(many_body_operator const& op) {
|
|
bool is_new_monomial;
|
|
typename monomials_map_t::iterator it;
|
|
for (auto const& m : op.monomials) {
|
|
std::tie(it, is_new_monomial) = monomials.insert(m);
|
|
if (!is_new_monomial) {
|
|
it->second += m.second;
|
|
erase_zero_monomial(monomials, it);
|
|
}
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
many_body_operator& operator-=(many_body_operator const& op) {
|
|
bool is_new_monomial;
|
|
typename monomials_map_t::iterator it;
|
|
for (auto const& m : op.monomials) {
|
|
std::tie(it, is_new_monomial) = monomials.insert(std::make_pair(m.first, -m.second));
|
|
if (!is_new_monomial) {
|
|
it->second -= m.second;
|
|
erase_zero_monomial(monomials, it);
|
|
}
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
many_body_operator& operator*=(many_body_operator const& op) {
|
|
monomials_map_t tmp_map; // product will be stored here
|
|
for (auto const& m : monomials)
|
|
for (auto const& op_m : op.monomials) {
|
|
// prepare an unnormalized product
|
|
monomial_t product_m;
|
|
product_m.reserve(m.first.size() + op_m.first.size());
|
|
for (auto const& op : m.first) product_m.push_back(op);
|
|
for (auto const& op : op_m.first) product_m.push_back(op);
|
|
// std::copy(m.first.begin(), m.first.end(), std::back_inserter(product_m));
|
|
// std::copy(op_m.first.begin(), op_m.first.end(), std::back_inserter(product_m));
|
|
normalize_and_insert(product_m, m.second * op_m.second, tmp_map);
|
|
}
|
|
std::swap(monomials, tmp_map);
|
|
return *this;
|
|
}
|
|
|
|
// implementation details of dagger
|
|
//
|
|
private:
|
|
static double _dagger(double x) { return x; }
|
|
static std::complex<double> _dagger(std::complex<double> x) { return conj(x); }
|
|
|
|
static canonical_ops_t _dagger(canonical_ops_t const& cop) {
|
|
return {!cop.dagger, cop.indices};
|
|
}
|
|
|
|
static monomial_t _dagger(monomial_t const& m) {
|
|
monomial_t res;
|
|
for (auto it = m.rbegin(); it != m.rend(); ++it) res.push_back(_dagger(*it));
|
|
return res;
|
|
}
|
|
|
|
public:
|
|
// dagger
|
|
friend many_body_operator dagger(many_body_operator const& op) {
|
|
many_body_operator res;
|
|
for (auto const& x : op) res.monomials.insert({_dagger(x.monomial), _dagger(x.coef)});
|
|
return res;
|
|
}
|
|
|
|
// Boost.Serialization
|
|
friend class boost::serialization::access;
|
|
template <class Archive> void serialize(Archive& ar, const unsigned int version) { ar& monomials; }
|
|
|
|
private:
|
|
// Normalize a monomial and insert into a map
|
|
static void normalize_and_insert(monomial_t& m, scalar_t coeff, monomials_map_t& target) {
|
|
// The normalization is done by employing a simple bubble sort algorithms.
|
|
// Apart from sorting elements this function keeps track of the sign and
|
|
// recursively calls itself if a permutation of two operators produces a new
|
|
// monomial
|
|
if (m.size() >= 2) {
|
|
bool is_swapped;
|
|
do {
|
|
is_swapped = false;
|
|
for (std::size_t n = 1; n < m.size(); ++n) {
|
|
canonical_ops_t& prev_index = m[n - 1];
|
|
canonical_ops_t& cur_index = m[n];
|
|
if (prev_index == cur_index) return; // The monomial is effectively zero
|
|
if (prev_index > cur_index) {
|
|
// Are we swapping C and C^+ with the same indices?
|
|
// A bit ugly ...
|
|
canonical_ops_t cur_index_flipped_type(cur_index);
|
|
cur_index_flipped_type.dagger = !cur_index_flipped_type.dagger;
|
|
if (prev_index == cur_index_flipped_type) {
|
|
monomial_t new_m;
|
|
new_m.reserve(m.size() - 2);
|
|
std::copy(m.begin(), m.begin() + n - 1, std::back_inserter(new_m));
|
|
std::copy(m.begin() + n + 1, m.end(), std::back_inserter(new_m));
|
|
normalize_and_insert(new_m, coeff, target);
|
|
}
|
|
coeff = -coeff;
|
|
std::swap(prev_index, cur_index);
|
|
is_swapped = true;
|
|
}
|
|
}
|
|
} while (is_swapped);
|
|
}
|
|
|
|
// Insert the result
|
|
bool is_new_monomial;
|
|
typename monomials_map_t::iterator it;
|
|
std::tie(it, is_new_monomial) = target.insert(std::make_pair(m, coeff));
|
|
if (!is_new_monomial) {
|
|
it->second += coeff;
|
|
erase_zero_monomial(target, it);
|
|
}
|
|
}
|
|
|
|
// Erase a monomial with a close-to-zero coefficient.
|
|
static void erase_zero_monomial(monomials_map_t& m, typename monomials_map_t::iterator& it) {
|
|
if (std::abs(it->second) < 100*std::abs(threshold)) m.erase(it);
|
|
}
|
|
|
|
struct print_visitor : public boost::static_visitor<> {
|
|
std::ostream& os;
|
|
print_visitor(std::ostream& os_) : os(os_) {}
|
|
template <typename T> void operator()(T const& x) const { os << x; }
|
|
};
|
|
|
|
friend std::ostream& operator<<(std::ostream& os, canonical_ops_t const& op) {
|
|
if (op.dagger) os << "^+";
|
|
os << "(";
|
|
int u = 0;
|
|
for (auto const& i : op.indices) {
|
|
if (u++) os << ",";
|
|
boost::apply_visitor(print_visitor{os}, i);
|
|
}
|
|
return os << ")";
|
|
}
|
|
|
|
friend std::ostream& operator<<(std::ostream& os, monomial_t const& m) {
|
|
for (auto const& c : m) {
|
|
os << "C" << c;
|
|
}
|
|
return os;
|
|
}
|
|
|
|
// Print many_body_operator itself
|
|
friend std::ostream& operator<<(std::ostream& os, many_body_operator const& op) {
|
|
if (op.monomials.size() != 0) {
|
|
bool print_plus = false;
|
|
for (auto const& m : op.monomials) {
|
|
os << (print_plus ? " + " : "") << m.second;
|
|
if (m.first.size()) os << "*";
|
|
os << m.first;
|
|
print_plus = true;
|
|
}
|
|
} else
|
|
os << "0";
|
|
return os;
|
|
}
|
|
};
|
|
|
|
|
|
// ---- factories --------------
|
|
|
|
// Free functions to make creation/annihilation operators
|
|
template <typename... IndexTypes> many_body_operator<double> c(IndexTypes... indices) {
|
|
return many_body_operator<double>::make_canonical(false, many_body_operator<double>::indices_t{indices...});
|
|
// need to put many_body_operator<double>::indices_t because {} constructor is explicit !?
|
|
}
|
|
|
|
template <typename... IndexTypes> many_body_operator<double> c_dag(IndexTypes... indices) {
|
|
return many_body_operator<double>::make_canonical(true, many_body_operator<double>::indices_t{indices...});
|
|
}
|
|
|
|
template <typename... IndexTypes> many_body_operator<double> n(IndexTypes... indices) {
|
|
return c_dag(indices...) * c(indices...);
|
|
}
|
|
}
|
|
}
|