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

Python reference manual

• Lattice Green’s functions
• Lindhard non-interacting generalized susceptibility
• Random Phase Approximation
• Impurity susceptibility and Bethe-Salpeter Equation
• Lattice Bethe-Salpeter Equation
• GW approximation
• Linearized Eliashberg equation
• Hubbard atom analytic response functions
• Two-particle response function linear-algebra operations
• Wannier90 tight binding parsers
• Tight binding lattice model
• Hartree-Fock and Hartree solvers
• Parameter collections

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
  • Anomalous Green’s Functions
  • Dyson-Gorkov Equations
  • Anomalous self-energy and particle-particle vertex
  • Linearization in \(\Delta\)
  • RPA Approach

FAQs

• Frequently-asked questions
  • Q: Why is not feature X implemented?