Input Options¶

PAUXY can be used either as a library or run with the usual “binary” + input file mode. Here we will describe the input options necessary in both cases.

Input File¶

A standard input file for pauxy is made up of a json dict like that below:

{
    "model": { },
    "qmc_options": { },
    "trial_wavefunction": { },
    "propagator": { },
    "estimates": {
        "mixed": { },
        "back_propagated": { },
        "itcf": { }
    }
}

Model Options¶

Currently it is only possible to simulate the Hubbard model (1d or 2d), or a generic system specified by a file containing the necessary one- and two-electron integrals.

Common Options¶

name

type: string

Name of model. Options: Hubbard or Generic.

Hubbard Model¶

t

type: float

Default 1.0.

Hubbard hopping integral.

U

type: float

Default 1.0

Hubbard U.

nx

type: int

Required.

Number of lattice sites in x direction.

ny

type: int

Required.

Number of lattice sites in y direction.

nup

type: int

Required.

Number of spin up electrons.

ndown

type: int

Required.

Number of spin down electrons.

Generic¶

integrals

type: string

Required.

Path to file containing one- and two-electron integrals. We assume an ascii FCIDUMP format as outlined, for example, here. Note that we currently only can treat real integrals.

decomposition

type: string

Optional.

Method by which we decompose two-electron integrals. Options:

cholesky Use cholesky decomposition. Default.

eigenvalue Use eigenvalue decomposition. Not implemented.

threshold : float: Cutoff for cholesky decomposition or minimum eigenvalue.
verbose : bool: Print extra information.

nup

type: int

Required.

Number of spin up electrons.

ndown

type: int

Required.

Number of spin down electrons.

QMC options¶

dt

type: float

Required.

Timestep.

nsteps

type: int

Required.

Total number of Monte Carlo steps to perform.

nmeasure

type: int

Required.

Number of steps between measurement.

nwalkers

type: int

Required.

Total number of walkers. If run in parallel then the number of walkers per core will be nwalkers / ncores.

npop_control

type: int

Default 10.

Number of steps between population control.

rng_seed

type: int

Optional.

Random number seed. Defaults to that calculated from system parameters via numpy.

Trial Wavefunction Options¶

The trial wavefunction controls the constraint in CPMC and phaseless AFQMC and can considerably affect results.

Common Options¶

The following options are common to all types of trial wavefunction.

name

type: string

Required.

Currently we support the following options:

free_electron trial wavefunction found by diagonalising the corresponding one-electron part of the Hamiltonian.

UHF Constructs the trial wavefunction from the UHF solution to the Hubbard model. Only implemented for the Hubbard model.

multi_determinant Reads a multi-determinant trial wavefunction from an input file.

hartree_fock Constructs Hartree–Fock trial wavefunction assuming our one-electron basis is a set of molecular Hartree–Fock orbitals. Note this is the recommended (over the free_electron) option when simulating a generic model system.

initial_wavefunction

type: string

Optional.

Specifies whether or not to use the trial wavefunction as the initial walker’s Slater Determinant or to use a free-electron like state. Options free_electron or trial. Default free_electron.

Free Electron Options¶

read_in

type: string

Optional.

Input file to read trial wavefunction from. Default None. Assumes a single SD in either .npy file format or in column major fortran format which assumes complex numbers.

UHF options¶

ninitial

type: int

Optional.

Number of random initial starting points for minimisation process. A simple attempt to attempt to find a global minimum. Default: 10.

nconv

type: int

Optional.

Maximum number of steps in a single self consistent cycle. Default 5000.

ueff

type: float

Optional.

Value of U to use for mean field Hamiltonian. Default 0.4.

deps

type: float

Optional.

Convergence threshold for energy between self consistentcy cycles.

alpha

type: float

Optional.

Mixing parameter. Default: 0.5.

verbose

type: bool

Optional.

Print extra information on convergence rate. Default: false.

Multi-Determinant options¶

type

type: string

Required.

Controls shape of SDs. Options: GHF or UHF. UHF SDs are of shape (M,N) while GHF SDs are of shape (2M,N) where M is the number of basis functions.

orbitals

type: string

Required.

File containing orbitals. Currently assumes fortran (column major) format in data file with one (fortran fomatted) complex number per line.

coefficients

type: string

Required.

File containing multi-determinant expansion coefficients. Expects one (fortran formatted) complex number per line.

Propagator Options¶

free_projection

type: bool

Default False.

Whether to perform free projection or not.

hubbard_stratonovich

type: string

Default None.

Type of Hubbard-Stratonovich transformation to use. Options: discrete, continuous or generic. See ref:theory/hubbard_stratonovich for an explanation.

Estimator Options¶

By default we estimate basic (mixed) estimators. More sophisticated estimators can be calculated using the optional mixed, back_propagated and itcf dictionaries through which we can estimate mixed estimates, back propagated quantities and imaginary time correlation functions.

Common Options¶

filename

type: string

Optional.

Output filename to which all estimators will be written (in hdf5 format.). Default: estimates.0.h5.

overwrite

type: string

Optional.

If true and if no filename is specified then any further calculations will overwrite the default output file. If false then output will be written to a file whose index is one greater than the most recent output file. Default: true.

Mixed¶

rdm

type: bool

Optional

If true then the one-particle green’s function is output to file. Default: false.

Back Propagated Options¶

nback_prop

type: int

Required.

Number of back propagation steps to perform. This times the timestep determines the back propagation time.

rdm

type: bool

Optional

If true then the one-particle green’s function is output to file. Default: false.

ITCF Options¶

tmax

type: float

Required.

Maximum value of imaginary time to calculate ITCF to.

stable

type: bool

Optional.

If true use the stabalised algorithm of Feldbacher and Assad. Default: true.

mode

type: string / list

Optional.

How much of the ITCF to save to file. Options include:

full print full ITCF.

diagonal print diagonal elements of ITCF.

elements print select elements defined from list.

Default: false.

kspace

type: bool

Optional.

If true also evaluate correlation functions in momentum space. Default false.