Features

The main features of the core components (i.e., quantum impurity solvers) of the iQIST software package are as follows:

• Model
  • Density-density interaction
  • General interaction (Slater or Kanamori scheme)^[01]
  • Spin-orbital coupling and crystal field splitting^[02]
  • Hubbard-Holstein model^[03]
  • Frequency-dependent Coulomb interaction^[04]

• Measurement tricks
  • Orthogonal polynomial representation (Legendre and Chebyshev polynomials)^[05]
  • Kernel polynomial representation^[06]
  • Improved estimator for self-energy function^[07]

• Observables
  • Single-particle Green's function in imaginary time space
  • Single-particle Green's function in matsubara frequency space
  • Two-particle correlation function in matsubara frequency space (experimental)^[08]
  • Local irreducible vertex function in matsubara frequency space (experimental)^[09]
  • Pair susceptibility in matsubara frequency space (experimental)^[10]
  • Self-energy function in matsubara frequency space
  • Histogram of perturbation expansion order
  • Kurtosis and skewness of perturbation expansion order
  • Kinetic and potential energies
  • Orbital occupation numbers^[11]
  • Double occupation numbers^[12]
  • Magnetic moment
  • Atomic state probability
  • Spin-spin correlation function in imaginary time space^[13]
  • Spin-spin correlation function in matsubara frequency space^[13]
  • Orbital-orbital correlation function in imaginary time space^[14]
  • Orbital-orbital correlation function in matsubara frequency space^[14]
  • Fidelity susceptibility^[15]
  • Kinetic energy fluctuation $\langle k^2\rangle - \langle k\rangle^2 - \langle k\rangle$^[16]

• Fast algorithms
  • Segment algorithm for density-density interaction^[17]
  • Divide-and-conquer algorithm^[18]
  • Sparse matrix multiplication^[19]
  • Good quantum numbers ($N, S_z, J_z$, PS)^[20]
  • Lazy trace evaluation^[21]
  • Dynamical truncation approximation^[22]
  • Newton-Leja polynomial interpolation algorithm (experimental)^[23]

• Parallelism
  • MPI
  • OpenMP^[24]

• API
  • Python binding
  • Input file generator by Python
  • Fortran binding

• Preprocessing
  • Atomic eigenvalue problem solver^[25]

• Postprocessing
  • Maximum entropy method^[26]
  • Stochastic analytical continuation^[27]
  • Kramers-Kronig transformation^[28]
  • Pade approximation^[29]
  • Polynomial fitting for self-energy function^[30]
  • Many tools and scripts, etc.