Documentation

Tutorials

• Square lattice susceptibility and the Random Phase Approximation (RPA)
• Bethe-Salpeter Equation (BSE) on the Hubbard atom
• Lattice Bethe-Salpeter Equation (BSE)
• DMFT lattice susceptibility
• Linearized Eliashberg equation on the attractive Hubbard model
• Solving the linearized Eliashberg equation in the random phase approximation limit

Python reference manual

• Lattice Green’s functions
  • lattice_dyson_g0_wk()
  • lattice_dyson_g_wk()
  • lattice_dyson_g_w()
• Lindhard non-interacting generalized susceptibility
  • lindhard_chi00_wk()
• 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()
• GW approximation
  • dynamical_screened_interaction_W_wk()
  • dynamical_screened_interaction_W_wk_from_generalized_susceptibility()
  • bubble_PI_wk()
  • gw_sigma_wk()
• 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
  • create_square_lattice()
  • TBSuperLattice
• Hartree-Fock and Hartree solvers
  • HartreeFockSolver
  • HartreeFockResponse
  • HartreeSolver
  • HartreeResponse
• Parameter collections
  • ParameterCollection
  • ParameterCollections
  • parameter_scan()

C++ reference manual

• Lattice Green’s functions
• Lindhard non-interacting generalized susceptibility
• Random Phase Approximation
• Generalized impurity susceptibility
• Generalized bubble susceptibility (for RPA)
• Generalized susceptibility and the Bethe-Salpeter equation
• GW approximation
• Linearized Eliashberg equation
• Hubbard atom analytic response functions
• Two-particle response function linear-algebra operations

Theory and notation

• Response function notation
  • Abbreviated 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 vertext \(F\)
• 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
• Generalized Kubo-Martin-Schwinger (KMS) boundary conditions
• Linear response from generalized susceptibility
• Linear response from applied external field
  • Reconstructing \(\chi\) from \(R\)
• Random phase approximation (RPA)
  • Interaction
  • RPA tensor
• 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?