Monte Carlo database on quantum spin models

Monte Carlo Database on Quantum Spin Models

QMC (DSQSS) result of S=1/2 and S=1 XXZ quantum spin model on the chain lattice and the square lattice;

$$ \mathcal{H} = -\sum_{\left\langle ij \right\rangle} \left[ J^z S_i^z S_j^z + \frac{J^{xy}}{2} \left( S_i^+S_j^- + S_i^-S_j^+ \right) \right] - h\sum_i S_i^z. $$

A plotting tool with x and y variables taken from the specified file (, which is written in the "plot_dsqss.config" file by default) is bundled.

Dataset

Dataset for XXZ model on the chain lattice and the square lattice is available as Dat/DSQSS_results_release_20231219.txt Meanings of the columns will be described later.

Usage of Plotting tool:

   $ perl plot.pl [datfile] [-f config file] [-v] [-x]

Dataset file, [datfile], contains at least 2 columns. By editing the config file, the user can specify which columns are used for x and y variables.

List of options

• -f: specify configuration file
• -v: say verbosely
• -x: extract data into file without plotting

Configuration file

Configuration is specified in the KEYWORD :: VALUE format.

Keywords

• OUTDIR: The directory where output files are saved.
• DATFILE: Input file
• XPLOT: The column name of data for x-axis
• YPLOT: The column name of data for y-axis
• DPLOT: The column name of data for errorbar in y-axis
• CONDITION: Only the data (row of dataset file) satisfying this condition are used
• LEGEND: The legend of the plot (curve)
• PLOTID: Used for filename
• BEFOREPLOT: Before plot, this gnuplot command is invoked
• AFTERPLOT: After plot, this gnuplot command is invoked

Values

• Name surrounded by a square bracket, e.g., [beta], means a column name in the datafile.
  • Available names are described later.
• A formula can be used, e.g., 1/[beta]
• In a strings, variables and/or formulas can be interpolated by using so-called printf format.
  • For example, "L=%4d", [L] is transformed as "L=32" for L=32 data.

Available columns:

The first $n means that this is in n-th column of the dataset file

Model parameter

$1 dim: Dimension $2 twoS: double of the spin size, for example, 1 for S=1/2. $3 Jz: coupling constant, negative for AF. $4 Jxy: coupling constant, negative for AF. $5 L: The size of the lattice. $6 beta: Inverse temperature. $7 h: Magnetic field. $8 bc: The boundary condition of the lattice.

Simulation parameter

$9 nset: The number of Monte Carlo sets. $10 NCYC: the number of cycles in One Monte Carlo sweep $11 npre: The number of Monte Carlo steps in the pre-calculation phase where the number of creation trials of a pair of worms in one Monte Carlo sweep is defined. $12 ntherm: The number of Monte Carlo sweeps to thermalize the system. $13 nmcs: The number of Monte Carlo sweeps to calculate mean values of observables. $14 seed: The seed of the random number generator $15 version: DSQSS version

Simulation environment parameter

The calculation is performed by using Supercomputer System-B (ohtaka) of ISSP, Univ. of Tokyo. The followings are the parameters for simulation environment

$16 queue: The name of queue of job scheduler $17 nnode: The number of calculation nodes $18 ntask: The number of MPI processes $19 ncpu_per_task: The number of process (threads) per one MPI process $20 time_limit: Assigned time of a job $21 time_elapsed: Elapsed time of a job $22 ID: Job ID

Observables

• *_a: The expectation value.
• *_d: The statistical error.

$23,24 sign: The sign of the weights. $25,26 anv: The mean number of the vertices. $27,28 ene: The energy density (energy per site). $29,30 spe: The specific heat. $31,32 som: The ratio of the specific heat and the temperature. $33,34 len: The mean length of worm. $35,36 xmx: The transverse susceptibility. $37,38 amzu: The “magnetization” (uniform, 𝜏 = 0). $39,40 bmzu: The “magnetization” (uniform, average over 𝜏 ). $41,42 smzu: The structure factor (uniform). $43,44 xmzu: The longitudinal susceptibility (uniform). $45,46 ds1: The derivative of "amzu" w.r.t. temperature times temperature. $47,48 wi2: The winding number. $49,50 rhos: The superfluid density. $51,52 time: The time in a Monte Carlo sweep (in seconds). $53,54 nsegmax: The maximum number of world-line segments. $55,56 nvermax: The maximum number of vertices.

See also the DSQSS manual for the detail. (https://www.pasums.issp.u-tokyo.ac.jp/dsqss/doc-manual)

Example:

For example, the magnetic field dependence the magnetization of the $S=1/2$ antiferromagnetic Heisenberg model on a square lattice can be plotted as follows.

(plot_dsqss.config)

OUTDIR     :: Plot<br>
DATFILE    :: Dat/DSQSS_results_release_20231219.txt

XPLOT      :: [h]<br>
YPLOT      :: [amzu_a]<br>
DPLOT      :: [amzu_d]<br>
PLOTID     :: "L%04dB%06d", [L], 1000*[beta]<br>
LEGEND     :: "L=%4d B=%10.3f" , [L] , [beta]<br>
CONDITION  :: [dim]==2 && [twoS]==1 && [L]<=64 && [beta]<=32 && [h]>=0

Copyright and license

The dataset and script are distributed under CC-BY 4.0 and GNU GPLv3, respectively.

Copyright 2023, Naoki Kawashima