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 splitting⁰²
  • Hubbard-Holstein model⁰³
  • Frequency-dependent Coulomb interaction⁰⁴

• Measurement tricks
  • Orthogonal polynomial representation (Legendre and Chebyshev polynomials)⁰⁵
  • Kernel polynomial representation⁰⁶
  • Improved estimator for self-energy function⁰⁷

• 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 numbers¹¹
  • Double occupation numbers¹²
  • Magnetic moment
  • Atomic state probability
  • Spin-spin correlation function in imaginary time space¹³
  • Spin-spin correlation function in matsubara frequency space¹³
  • Orbital-orbital correlation function in imaginary time space¹⁴
  • Orbital-orbital correlation function in matsubara frequency space¹⁴
  • Fidelity susceptibility¹⁵
  • Kinetic energy fluctuation $\langle k^2\rangle - \langle k\rangle^2 - \langle k\rangle$¹⁶

• Fast algorithms
  • Segment algorithm for density-density interaction¹⁷
  • Divide-and-conquer algorithm¹⁸
  • Sparse matrix multiplication¹⁹
  • Good quantum numbers ($N, S_z, J_z$, PS)²⁰
  • Lazy trace evaluation²¹
  • Dynamical truncation approximation²²
  • Newton-Leja polynomial interpolation algorithm (experimental)²³

• Parallelism
  • MPI
  • OpenMP²⁴

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

• Preprocessing
  • Atomic eigenvalue problem solver²⁵

• Postprocessing
  • Maximum entropy method²⁶
  • Stochastic analytical continuation²⁷
  • Kramers-Kronig transformation²⁸
  • Pade approximation²⁹
  • Polynomial fitting for self-energy function³⁰
  • Many tools and scripts, etc.

Additional Limitations:

⁰¹ Only for the BEGONIA, LAVENDER, CAMELLIA, PANSY, and MANJUSHAKA.

⁰² Only for the BEGONIA, LAVENDER, PANSY, and MANJUSHAKA.

⁰³ Only for the NARCISSUS.

⁰⁴ Only for the NARCISSUS.

⁰⁵ Only for the GARDENIA, NARCISSUS, LAVENDER, CAMELLIA, and MANJUSHAKA.

⁰⁶ Only for the GARDENIA, NARCISSUS, LAVENDER, CAMELLIA, and MANJUSHAKA.

⁰⁷ Only for the GARDENIA and NARCISSUS.

⁰⁸ Only for the GARDENIA, NARCISSUS, LAVENDER, CAMELLIA, and MANJUSHAKA.

⁰⁹ Only for the GARDENIA, NARCISSUS, LAVENDER, CAMELLIA, and MANJUSHAKA.

¹⁰ Only for the GARDENIA, NARCISSUS, LAVENDER, CAMELLIA, and MANJUSHAKA.

¹¹ Only for the AZALEA, GARDENIA, and NARCISSUS.

¹² Only for the AZALEA, GARDENIA, and NARCISSUS.

¹³ Only for the GARDENIA and NARCISSUS.

¹⁴ Only for the GARDENIA and NARCISSUS.

¹⁵ Only for the GARDENIA, NARCISSUS, LAVENDER, CAMELLIA, and MANJUSHAKA.

¹⁶ Only for the GARDENIA, NARCISSUS, LAVENDER, CAMELLIA, and MANJUSHAKA.

¹⁷ Only for the AZALEA, GARDENIA, and NARCISSUS.

¹⁸ Only for the BEGONIA, LAVENDER, PANSY, and MANJUSHAKA.

¹⁹ Only for the BEGONIA, LAVENDER, and CAMELLIA.

²⁰ Only for the PANSY and MANJUSHAKA.

²¹ Only for the MANJUSHAKA.

²² Only for the MANJUSHAKA.

²³ Only for the CAMELLIA.

²⁴ Only for the measurement of two-particle quantities.

²⁵ Only for the JASMINE.

²⁶ Only for the HIBISCUS.

²⁷ Only for the HIBISCUS.

²⁸ Only for the HIBISCUS.

²⁹ Only for the HIBISCUS.

³⁰ Only for the HIBISCUS.