5.2.2. Make an input file for DSQSS/PMWA

To execute PMWA, a text format input file is required. There are two kinds of parameters in the input file: parameters specifying calculation conditions and parameters specifying a Hamiltonian.

An example of the input file is shown below:

RUNTYPE = 0
NSET   = 10
NMCS   = 10000
NPRE   = 10000
NTHERM = 10000
NDECOR = 10000
SEED  = 31415
NC    = 0
NVERMAX = 10000000
NWORMAX = 1000
latfile   = lattice.xml
outfile   = sample.log
CB      = 2
G       = 0.3
U       = 0
V       = 3
t       = 1
MU      = 2
NMAX    = 1

The meaning of each parameter is as follows.

  • Parameter of calculation conditions

    Parameter

    type

    Remarks

    RUNTYPE

    int

    Calculation mode (0: normal calculation, 1: restart calculation)

    CB

    int

    Initial arrangement (0: Vacuum, 1: Checker-Board, 2: Random)

    NSET

    int

    The repetition number of Monte Carlo calculation

    NMCS

    int

    The number of Monte Carlo sweeps used for physical quantity calculation

    NPRE

    int

    The number of Monte Carlo steps used for precalculation to determine the number of trials to generate worms per sweep

    NMCSE

    int

    The number of Monte Carlo sweeps used for initial relaxation

    NMCSD

    int

    The number of Monte Carlo sweeps between measurements

    SEED

    int

    If it is 0 or more, seed is actually used, if negative, seed is given with random number.

    NVERMAX

    int

    The maximum number of vertexes (default is \(10^8\) ). There is no upper limit when -1.

    NWORMAX

    int

    The maximum number of worms (default is \(10^3\) ). There is no upper limit when -1.

    SFINPFILE

    str

    If this file name is given, calculate structure factors specified in this file.

    SFOUTFILE

    str

    If SFINPFILE is given, output structure factors to the specified file (default is sf.out).

    Step_x

    int

    Give the spatial width when computing the correlation function (default: 1).

    Step_k

    int

    Give the width of wavenumber when computing correlation function of wavenumber representation (default: 1).

    CFOUTFILE

    str

    When it is input, it outputs the correlation function to the specified file (default is cf.out).

Here, NVERMAX and NWORMAX are automatically resized and determined (implemented in ver. 1.2.0).

  • Parameter of interactions

PMWA can treat the models for hard-core boson and \(S=1/2\) XXZ system. The Hamiltonian for hard-core boson system is given by

\[\begin{split}{\cal H} &= -t_{b} \sum_{\langle i, j\rangle}b_i^{\dagger} b_j + U_{BB}\sum_i n_i(n_i -1) +V_{B1}\sum_{\langle i, j\rangle} n_i n_j \\ &+\mu\sum_i n_i-\Gamma\sum_i(b_i^{\dagger}+b_i),\end{split}\]

where \(\langle i,j \rangle\) indicates a nearest-neighbor pair. For \(S=1/2\) XXZ model, the hamiltonian is given by

\[{\cal H}^{XXZ} = -J_{xy} \sum_{\langle i, j\rangle}(S_i^x S_j^x + S_i^y S_j^y)-J_z\sum_{\langle i, j\rangle}S_i^zS_j^z-H \sum_{i}S_{i}^z -\Gamma \sum_i S_i^x.\]

The parameters specified in the input file and the parameters in the above expression correspond as follows.

Parameter

Boson

Spin

t

\(t_b\)

\(J_{xy}\)

U

\(U_{BB}\)

-

V

\(V_{B1}\)

\(J_{z}\)

MU

\(\mu\)

\(H\)

G

\(\Gamma\)

\(\Gamma/2\)

Each parameter is specified as double type.