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QInchworm.jl

The package QInchworm.jl is a Julia implementation of the quasi Monte Carlo variant1 of the inchworm algorithm2 for solving impurity models with multiple interacting fermions. Using quasi Monte Carlo, a 1/N convergence rate with the number of samples is achievable, which compares favorably to the 1/\sqrt{N} convergence of the Monte Carlo methods.

Below, you can find an API reference of QInchworm.jl's modules. Some parts of the API, such as handling of the atomic problem and of the pair interactions/hybridization, depend on container types from Keldysh.jl and exact diagonalization tools of KeldyshED.jl.

There is also an [example page](@ref example) showing how to use QInchworm.jl to solve a quantum impurity problem in thermodynamic equilibrium and to compute two-point correlation functions for it.

Public API

  • [QInchworm.expansion](@ref api:QInchworm.expansion)
  • [QInchworm.inchworm](@ref api:QInchworm.inchworm)
  • [QInchworm.randomization](@ref api:QInchworm.randomization)
  • [QInchworm.ppgf](@ref api:QInchworm.ppgf)
  • [QInchworm.spline_gf](@ref api:QInchworm.spline_gf)
  • [QInchworm.utility](@ref api:QInchworm.utility)

Internals

  • [QInchworm.expansion](@ref QInchworm.expansion)
  • [QInchworm.inchworm](@ref QInchworm.inchworm)
  • [QInchworm.ppgf](@ref QInchworm.ppgf)
  • [QInchworm.sector_block_matrix](@ref QInchworm.sector_block_matrix)
  • [QInchworm.spline_gf](@ref QInchworm.spline_gf)
  • [QInchworm.utility](@ref QInchworm.utility)
  • [QInchworm.mpi](@ref QInchworm.mpi)
  • [QInchworm.scrambled_sobol](@ref QInchworm.scrambled_sobol)
  • [QInchworm.qmc_integrate](@ref QInchworm.qmc_integrate)
  • [QInchworm.randomization](@ref QInchworm.randomization)
  • [QInchworm.diagrammatics](@ref QInchworm.diagrammatics)
  • [QInchworm.topology_eval](@ref QInchworm.topology_eval)

Footnotes

  1. Inchworm quasi Monte Carlo for quantum impurities. Hugo U. R. Strand, Joseph Kleinhenz and Igor Krivenko. arXiv:2310.16957. ↩

  2. [Taming the Dynamical Sign Problem in Real-Time Evolution of Quantum Many-Body Problems. Guy Cohen, Emanuel Gull, David R. Reichman, and Andrew J. Millis. Phys. Rev. Lett. 115, 266802 (2015).] (https://link.aps.org/doi/10.1103/PhysRevLett.115.266802) ↩