dft_tools/triqs/lattice/tight_binding.hpp

/*******************************************************************************
 *
 * 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/>.
 *
 ******************************************************************************/
#pragma once
#include "brillouin_zone.hpp"
#include <triqs/utility/complex_ops.hpp>

namespace triqs {
namespace lattice {

 /**
   For tightbinding Hamiltonian with fully localised orbitals
   Overlap between orbital is taken as unit matrix.
  */
 class tight_binding {

  bravais_lattice bl_;
  std::vector<std::vector<long>> all_disp;
  std::vector<matrix<dcomplex>> all_matrices;

  public:
  ///
  tight_binding(bravais_lattice const& bl, std::vector<std::vector<long>> all_disp, std::vector<matrix<dcomplex>> all_matrices);

  /// Underlying lattice
  bravais_lattice const& lattice() const { return bl_; }

  /// Number of bands, i.e. size of the matrix t(k)
  int n_bands() const { return bl_.n_orbitals(); }

  // 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]);
  }

  // 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<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, 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);
}
}