4.1. Simple mode of DSQSS/DLA

A simple mode of DSQSS/DLA is the simplest workflow for DSQSS/DLA. In this mode, users can simulate of a predefined model on a predefined lattice from one text file. Fig. 4.1 shows a workflow of the simple mode.

Fig. 4.1 Simple mode of DSQSS/DLA. Ellipses are files and rectangles are tools.

4.1.1. Simple mode file std.toml

A simple mode file is a textfile written in TOML format. This is used as an input file of several tools such as dla_pre.

4.1.1.1. parameter

A table specifying simulation parameters such as the inverse temperature. This table is used in dla_pre and dla_pgen.

Keys in the parameter table are following:

name	type	default	description
beta	double	–	Inverse temperature.
npre	int	1000	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.
ntherm	int	1000	The number of Monte Carlo sweeps to thermalize the system.
ndecor	int	1000	The number of Monte Carlo sweeps to reduce autocorrelation time between two preceding sets.
nmcs	int	1000	The number of Monte Carlo sweeps to calculate mean values of observables.
nset	int	10	The number of Monte Carlo sets.
simulationtime	double	0.0	Simulation time in second.
seed	int	198212240	The seed of the random number generator.
nvermax	int	10000	The maximum number of vertices.
nsegmax	int	10000	The maximum number of world-line segments.
algfile	string	algorithm.xml	The filename of an algorithm file.
latfile	string	lattice.xml	The filename of a lattice file.
wvfile	string	–	A wavevector XML file. If it is an empty string, observables as functions of wavevector will not be calculated.
dispfile	string	–	A relative coordinates XML file. If it is an empty string, observables as functions of relative coordinates will not be calculated.
outfile	string	sample.log	The name of the main result file.
sfoutfile	string	sf.dat	The name of the structure factor result file.
cfoutfile	string	cf.dat	The name of the real space temperature Green’s function output file.
ckoutfile	string	ck.dat	The name of the momentum space temperature Green’s function output file.

• About simulationtime

  • When simulationtime > 0.0

  • DSQSS/DLA loads the checkpoint file and resumes the simulation if the checkpoint file exists. - If not, DSQSS/DLA starts a new simulation.

  • After the time specified by “simulationtime” (in seconds) has elapsed, DSQSS/DLA saves the state of the simulation into the checkpoint file and halts the simulation.

  • The name of the checkpoint file is that of the main result file with a suffix “.cjob”.

  • When simulationtime <= 0.0

    • The checkpoint file is ignored. DSQSS/DLA never saves nor loads it.

4.1.1.2. lattice

A table specifying information of lattice. This is used in dla_pre and dla_latgen.

Keys in the lattice table are following:

name	type	default	description
lattice	string	–	The type of lattice.
dim	int	–	Dimension.
L	list(int) or int	–	The size of the lattice. Specified by an integer or a list of integers. If the number of elements is less than the dimension, missing elements are filled by the last element of the given list.
bc	list(bool) or bool	true	The boundary condition of the lattice. Specified by a boolean or a list of booleans. true means the periodic boundary condition, false means the open boundary condition.

Available lattices are following.

hypercubic

A hyper cubic lattice with arbitrary dimension. By using bc, users can generate ladder or slab lattices.

triangular

A two dimensional triangular lattice.

honeycomb

A two dimensional honeycomb lattice.

kagome

A two dimensional kagome lattice.

4.1.1.3. hamiltonian

A table specifying information of Hamiltonian. This table is used in dla_pre and dla_hamgen.

Keys in the hamiltonian table are following:

name	type	default	description
model	string	–	The type of the model. ‘spin’ means XXZ spin model and ‘boson’ means Bose-Hubbard model.
M	int	1	For XXZ model twice as the length of the local spin, \(M=2S\), and for Bose-Hubbard model the cutoff of the number of particles on a site.

XXZ model

\[\mathcal{H} = \sum_{\langle i, j \rangle} -J_z S_i^z S_j^z -\frac{J_{xy}}{2} \left( S_i^+ S_j^- + S_i^- S_j^+ \right) + D \sum_i \left(S_i^z\right)^2 - h \sum_i S_i^z\]

has the following parameters:

name	type	default	description
Jz	list(float) or float	0.0	The exchange interaction. Positive for ferromagnetic and negative for antiferromagnetic.
Jxy	list(float) or float	0.0	The exchange interaction. Positive for ferromagnetic and negative for antiferromagnetic.
D	list(float) or float	0.0	The onsite uniaxial anisotropy.
h	list(float) or float	0.0	The magnetic field.

Bose-Hubbard model

\[\mathcal{H} = \sum_{\langle i, j \rangle} \left[ -t b_i^\dagger \cdot b_j + h.c. + V n_i n_j \right] + \sum_i \left[ \frac{U}{2} n_i(n_i-1) - \mu n_i \right]\]

has the following parameters:

name	type	default	description
t	list(float) or float	0.0	The hopping parameter.
V	list(float) or float	0.0	The offsite interaction. Positive for repulsion and negative for attraction.
U	list(float) or float	0.0	The onsite interaction. Positive for repulsion and negative for attraction.
mu	list(float) or float	0.0	The chemical potential.

4.1.1.4. kpoints

A table specifying information of wavevectors. This table is used in dla_pre and dla_wvgen.

Keys in the kpoints table are following:

name	type	default	description
ksteps	list(int) or int	0	Increments of wavenumber. If 0, half of lattice size instead of 0 is set.

4.1.1.5. algorithm

A table specifying algorithm for calculating scattering probability of wormheads. This table is used in dla_pre.

Keys in the algorithm table are following:

name	type	default	description
kernel	string	‘suwa todo’	Algorithm for calculating the scattering probability of wormheads.

Available kernel s are following:

suwa todo

Rejection minimized algorithm without detailed balance condition (irreversible) proposed by Suwa and Todo. (H. Suwa and S. Todo, PRL 105, 120603 (2010))

reversible suwa todo

Rejection minimized algorithm with detailed balance condition (reversible) proposed by Suwa and Todo. (arXiv:1106.3562)

heat bath

Heat bath method (Gibbs sampler).

metropolis

Metropolis-Hastings algorithm.