triqs_tprf
3.3.1
  • Packaged Versions of TPRF
    • Ubuntu Debian packages
    • Anaconda (experimental)
    • Docker
  • Compiling TPRF from source
    • Prerequisites
    • Installation steps
    • Version compatibility
    • Custom CMake options
  • Documentation
    • Tutorials
      • Square lattice susceptibility and the Random Phase Approximation (RPA)
        • Tight binding Hamiltonian
        • Dispersion \(\epsilon(\mathbf{k})\) and Fermi surface
        • Bare generalized susceptibility \(\chi_0\)
        • Physical response function \(\chi_{S_z, S_z}\)
        • Random phase approximation (RPA)
      • Bethe-Salpeter Equation (BSE) on the Hubbard atom
        • Single-particle Green’s function \(G_{\sigma \sigma'}(i\omega_n)\)
        • Bare and full susceptibility \(\chi_0\) and \(\chi\)
        • Bethe-Salpeter Equation (BSE) for \(\Gamma_m^{(PH)}\)
        • Analytic vertex \(\Gamma_m^{(PH)}\)
        • BSE frequency window convergence
      • Lattice Bethe-Salpeter Equation (BSE)
      • DMFT lattice susceptibility
        • Self consistent calculations in applied field
        • Lattice susceptibility from the Bethe-Salpeter Equation
          • DMFT local vertex
          • Lattice Bethe-Salpeter Equation
        • Summary
      • Spin susceptibility in Sr2RuO4
        • Dual Bethe-Salpeter equation
      • Linearized Eliashberg equation on the attractive Hubbard model
        • Hubbard model on a square lattice
          • Semi particle-hole transformation
        • Solving the linearized Eliashberg equation
      • Solving the linearized Eliashberg equation in the random phase approximation limit
        • 1. Construct the density- and magnetic-susceptibilties in RPA
        • 2. Construct the particle-particle vertex in RPA
        • 3. Construct the symmetrizing functions
          • Frequency: Even, Momentum: Even
          • Frequency: Odd, Momentum: Odd
        • 4. Solve the linearized Eliashberg equation
    • Python reference manual
      • Lattice Green’s functions
        • lattice_dyson_g0_wk()
        • lattice_dyson_g0_fk()
        • lattice_dyson_g_wk()
        • lattice_dyson_g_fk()
        • lattice_dyson_g_f()
        • lattice_dyson_g_w()
      • Non-interacting generalized susceptibility
        • imtime_bubble_chi0_wk()
        • lindhard_chi00()
      • Random Phase Approximation
        • solve_rpa_PH()
        • kanamori_quartic_tensor()
      • Impurity susceptibility and Bethe-Salpeter Equation
        • chi0_from_gg2_PH()
        • chi0_from_gg2_PP()
        • chi_from_gg2_PH()
        • chi_from_gg2_PP()
        • solve_local_bse()
      • Lattice Bethe-Salpeter Equation
        • solve_lattice_bse()
        • solve_lattice_bse_at_specific_w()
        • get_chi0_wnk()
        • get_chi0_nk_at_specific_w()
      • Dual Bethe-Salpeter Equation
        • solve_lattice_dbse()
        • impurity_reducible_vertex_F()
      • GW approximation
        • GWSolver
        • dynamical_screened_interaction_W()
        • dynamical_screened_interaction_W_from_generalized_susceptibility()
        • bubble_PI_wk()
        • gw_sigma()
        • g0w_sigma()
      • Linearized Eliashberg equation
        • solve_eliashberg()
        • preprocess_gamma_for_fft()
        • semi_random_initial_delta()
        • power_method_LR()
        • implicitly_restarted_arnoldi_method()
        • construct_gamma_singlet_rpa()
        • construct_gamma_triplet_rpa()
      • Hubbard atom analytic response functions
        • analytic_hubbard_atom()
      • Two-particle response function linear-algebra operations
        • inverse_PH()
        • inverse_PP()
        • inverse_PH_bar()
        • product_PH()
        • product_PP()
        • product_PH_bar()
        • identity_PH()
        • identity_PP()
        • identity_PH_bar()
      • Wannier90 tight binding parsers
        • parse_hopping_from_wannier90_hr_dat()
        • parse_lattice_vectors_from_wannier90_wout()
        • parse_reciprocal_lattice_vectors_from_wannier90_wout()
        • parse_band_structure_from_wannier90_band_dat()
      • Tight binding lattice model
        • TBLattice
          • TBLattice.dispersion()
          • TBLattice.fourier()
          • TBLattice.get_kmesh()
          • TBLattice.get_rmesh()
          • TBLattice.lattice_to_real_coordinates()
          • TBLattice.n_orbitals
          • TBLattice.ndim
          • TBLattice.orbital_names
          • TBLattice.orbital_positions
          • TBLattice.units
        • create_square_lattice()
        • TBSuperLattice
          • TBSuperLattice.change_coordinates_L_to_SL()
          • TBSuperLattice.change_coordinates_SL_to_L()
          • TBSuperLattice.cluster_sites()
          • TBSuperLattice.fold()
          • TBSuperLattice.pack_index_site_orbital()
          • TBSuperLattice.unpack_index_site_orbital()
      • Hartree-Fock and Hartree solvers
        • HartreeFockSolver
          • HartreeFockSolver.mat2vec()
          • HartreeFockSolver.solve_iter()
          • HartreeFockSolver.solve_newton()
          • HartreeFockSolver.solve_newton_mu()
          • HartreeFockSolver.vec2mat()
        • HartreeFockResponse
        • HartreeSolver
          • HartreeSolver.mat2vec()
          • HartreeSolver.vec2mat()
        • HartreeResponse
      • Utility functions
        • k_space_path()
        • chi_contraction()
      • Parameter collections
        • ParameterCollection
          • ParameterCollection.alter()
          • ParameterCollection.convert_keys_from_string_to_python()
          • ParameterCollection.copy()
        • ParameterCollections
        • parameter_scan()
    • C++ reference manual
      • Lattice Green’s functions
        • triqs_tprf::lattice_dyson_g0_wk
          • Parameters
          • Returns
        • triqs_tprf::lattice_dyson_g0_fk
          • Parameters
          • Returns
        • triqs_tprf::lattice_dyson_g_wk
          • Parameters
          • Returns
        • triqs_tprf::lattice_dyson_g_fk
          • Parameters
          • Returns
        • triqs_tprf::lattice_dyson_g_w
          • Parameters
          • Returns
        • triqs_tprf::fourier_wk_to_wr
          • Parameters
          • Returns
        • triqs_tprf::fourier_wr_to_wk
          • Parameters
          • Returns
        • triqs_tprf::fourier_wr_to_tr
          • Parameters
          • Returns
        • triqs_tprf::fourier_tr_to_wr
          • Parameters
          • Returns
      • Lindhard non-interacting generalized susceptibility
        • triqs_tprf::lindhard_chi00
          • Parameters
          • Returns
      • Random Phase Approximation
        • triqs_tprf::solve_rpa_PH
          • Parameters
          • Returns
      • Generalized impurity susceptibility
        • triqs_tprf::chi0_from_gg2_PH
          • Parameters
          • Returns
        • triqs_tprf::chi0_from_gg2_PP
          • Parameters
          • Returns
        • triqs_tprf::chi_from_gg2_PH
          • Parameters
          • Returns
        • triqs_tprf::chi_from_gg2_PP
          • Parameters
          • Returns
      • Generalized bubble susceptibility (for RPA)
        • triqs_tprf::chi0_tr_from_grt_PH
          • Parameters
          • Returns
        • triqs_tprf::chi0_w0r_from_grt_PH
          • Parameters
          • Returns
        • triqs_tprf::chi_w0r_from_chi_tr
          • Parameters
          • Returns
        • triqs_tprf::chi_wr_from_chi_tr
          • Parameters
          • Returns
        • triqs_tprf::chi_tr_from_chi_wr
          • Parameters
          • Returns
        • triqs_tprf::chi_wk_from_chi_wr
          • Parameters
          • Returns
        • triqs_tprf::chi_wr_from_chi_wk
          • Parameters
          • Returns
      • Generalized susceptibility and the Bethe-Salpeter equation
        • triqs_tprf::chi0r_from_gr_PH
          • Parameters
          • Returns
        • triqs_tprf::chi0r_from_gr_PH_nompi
          • Parameters
          • Returns
        • triqs_tprf::chi0q_from_g_wk_PH
          • Parameters
          • Returns
        • triqs_tprf::chi0r_from_chi0q
          • Parameters
          • Returns
        • triqs_tprf::chi0q_from_chi0r
          • Parameters
          • Returns
        • triqs_tprf::chi0q_sum_nu
          • Parameters
          • Returns
        • triqs_tprf::chi0q_sum_nu_tail_corr_PH
          • Parameters
          • Returns
        • triqs_tprf::chi0q_sum_nu_q
          • Parameters
          • Returns
        • triqs_tprf::chiq_from_chi0q_and_gamma_PH
          • Parameters
          • Returns
        • triqs_tprf::chiq_sum_nu_from_chi0q_and_gamma_PH
          • Parameters
          • Returns
      • GW approximation
        • triqs_tprf::dynamical_screened_interaction_W
          • Parameters
          • Returns
        • triqs_tprf::dynamical_screened_interaction_W_from_generalized_susceptibility
          • Parameters
          • Returns
        • triqs_tprf::gw_sigma
          • Parameters
          • Returns
        • triqs_tprf::g0w_sigma
          • Parameters
          • Returns
      • Linearized Eliashberg equation
        • triqs_tprf::eliashberg_product
          • Parameters
          • Returns
        • triqs_tprf::eliashberg_product_fft
          • Parameters
          • Returns
        • triqs_tprf::split_into_dynamic_wk_and_constant_k
          • Parameters
          • Returns
        • triqs_tprf::dynamic_and_constant_to_tr
          • Parameters
          • Returns
        • triqs_tprf::construct_phi_wk
          • Parameters
          • Returns
      • Hubbard atom analytic response functions
      • Two-particle response function linear-algebra operations
        • triqs_tprf::inverse
          • Template parameters
          • Parameters
          • Returns
        • triqs_tprf::product
          • Template parameters
          • Parameters
          • Returns
        • triqs_tprf::identity
          • Template parameters
          • Parameters
          • Returns
    • Theory and notation
      • Response function notation
        • Generalized susceptibility \(\chi\)
          • Bare generalized susceptibility \(\chi_0\)
          • Reducible vertex function \(F\)
          • Full generalized particle-hole susceptibility \(\chi\)
        • Bethe-Salpeter equations (BSE)
          • Matsubara frequency transforms
          • Particle-hole channel (\(PH\))
          • Crossed-Particle-particle channel (\(PPx\))
      • On the single particle Green’s function
        • Field operator Matsubara transforms
      • Vertex functions
        • Fully reducible vertex \(F\)
        • Bethe-Salpeter equations for the fully reducible vertex \(F\)
        • Matsubara frequency parametrization
        • Derivation: Product relations
          • Particle-Hole channel (\(PH\))
          • Vertical-Particle-Hole channel (\(\bar{PH}\))
          • Particle-Particle channel (\(PP\))
          • Crossed-Particle-Particle channel (\(PPx\))
      • (Anti-)Periodicity
        • Two-particle Green’s functions
      • Kubo-Martin-Schwinger (KMS) boundary conditions
        • Generalization to two-particle Green’s functions
      • Linear response
        • From the generalized susceptibility
        • From an applied external field
      • Random phase approximation (RPA)
        • Interaction
        • Antisymmetrized interaction tensor \(U\)
        • Spin-independent RPA calculations
          • Matrix RPA
          • Mapping between spin-dependent and independent quantities
          • Example
      • Linearized Eliashberg Equation
        • Deriving the linearized Eliashberg equation from the normal state
          • Relation to the BCS gap equation
        • Details for applications
          • SPOT Condition
          • Random phase approximation for the irreducible particle-particle vertex
    • FAQs
      • Frequently-asked questions
        • Q: Why is not feature X implemented?
  • Reporting issues
  • Changelog
    • Version 3.3.1
      • General
    • Version 3.3.0
      • General
      • gw
      • doc
      • cmake
    • Version 3.2.0
      • Dual Bethe-Salpeter Equation (DBSE)
      • Hedin’s GW approximation
      • Discrete Lehmann Representation (DLR) support
    • Version 3.1.1
      • General
      • py
      • doc
    • Version 3.1.0
    • Eliashberg
    • Bethe-Salpeter equation (BSE)
    • Chi0
    • Maintenance
    • TRIQS compatibility
    • Version 3.0.0
    • General
    • cmake
    • doc
    • py3
    • python
    • Version 2.2.0
    • doc
    • fourier
    • General
    • hf
    • Version 2.1.1
  • Authors
    • License
    • Disclaimer
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© Copyright 2017, H. U.R. Strand.