4.3. Input files for DSQSS/DLA

4.3.1. The list of input files

param.in

Parameter list for the simulation, e.g., the number of Monte Carlo sets.

lattice.xml

Definition of the lattice.

algorithm.xml

Definition of the algorithm (e.g., scattering rate of a worm).

wavevector.xml

Indication of wave vectors for structure factors. (optional)

displacement.xml

Indexing directions between all the sites. (optional)

4.3.2. Parameter file

The parameter file is a plain-text file with the following format,

  • One line stands for one parameter by the key-value style, <name> = <value>.

  • Cases are insensitive except for file names.

  • White spaces and blank lines are ignored.

  • Parts between “#” symbol and the linebreak are ignored as comments.

The list of parameters are the 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

100000

The maximum number of vertices.

nsegmax

int

100000

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.

ntau

int

10

The number of the discretization of the imaginary time for calculating some observables as functions of imaginary time.

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.

4.3.3. Lattice XML file lattice.xml

A lattice file is a textfile written in XML format. This defines space to be simulation, for example, the number of sites, the connections between sites, and so on. This file can be very complicated, so DSQSS has a utility tool dla_alg to generate lattice XML files from simpler files, lattice data files and lattice TOML files.

The lattice file has a unique element named “Lattice”. The other elements belong to “Lattice” as children.

Lattice

The root element.

Lattice/Comment

(Optional) Comment. DSQSS ignores this element.

Lattice/Dimension

The dimension of the lattice.

Lattice/LinearSize

The size of the lattice in units of the unitcell. This takes space-separated positive integers as many as specified by “Lattice/Dimension”.

<LinearSize> 3 4 </LinearSize>
# unitcells are arranged in 3x4.
Lattice/NumberOfSites

The number of sites.

Lattice/NumberOfInteractions

The number of the interactions. When all the interactions are two-body ones, this is nothing but the number of bonds.

Lattice/NumberOfSiteTypes

The number of site types.

Lattice/NumberOfInteractionTypes

The number of interaction types.

Lattice/NumberOfBondDirections

The number of bond directions.

Lattice/NumberOfEdgeInteractions

The number of bonds connecting sites over the lattice’s boundary.

Lattice/Basis

The basic vectors spanning lattice space.

Lattice/S

Site information. “Lattice” should includes this element as many as the number specified by “Lattice/NumberOfSites”. This takes two nonnegative integers, “index of site” and “site type”. The detail of site type is defined in an algorithm file.

<S> 3 0 </S>
# the site with index 3 has the site type of 0.
Lattice/I

Interaction information. “Lattice” should includes this element as many as the number specified by “Lattice/NumberOfInteractions”. This takes space-separated integers, “index of the interaction”, “interaction type”, “the number of sites involved in the interaction”, “indices of involved sites”. The details of interaction type, e.g., the strength, are defined in an algorithm file. The order of the indices of sites should be compatible with the order of sites specified in “Algorithm/Vertex/InitialConfiguration” in the algorithm file.

<I> 5 1 2 8 12 </I>
# the interaction with index 5 has the interaction type of 1 and connects 2 sites, 8 and 12.
Lattice/Direction

The direction of bonds. This takes “index of the direction” and “coordinates of the direction.”

4.3.4. Algorithm XML file algorithm.xml

An algorithm file is a textfile written in XML format. This defines the details of interactions, for example, the scattering probability of a worm head. This file can be very complicated, so DSQSS has a utility tool dla_alg to generate algorithm files from more simple file, the Hamiltonian file introduced later.

The algorithm file has a unique element named “Algorithm”. The other elements belong to “Algorithm” as children.

Algorithm

The root element. This has children, “General”, “Site”, “Interaction”, and “Vertex”.

Algorithm/Comment

(Optional) Comment. DSQSS ignores this.

Algorithm/General

General parameters such as the number of site types. This has children, “NSType”, “NIType”, “NVType”, “NXMax”, and “WDiag”.

<Algorithm>
  <General>
    <NSType>  1 </NSType>
    <NIType>  1 </NIType>
    <NVType>  2 </NVType>
    <NXMax>   2 </NXMax>
    <WDiag>   0.25 </WDiag>
  </General>
  ...
</Algorithm>
Algorithm/General/NSType

The number of site types.

Algorithm/General/NIType

The number of interaction types.

Algorithm/General/NVType

The number of vertex types.

Algorithm/General/NXMax

The maximum number of states on a site. For example, \(2S+1\) for a spin system with local spin \(S\).

Algorithm/General/WDiag

A coefficient to measure correlation functions from the length of worms.

Algorithm/Site

This defines a site type, for example, the weight of worm heads on a site. This has children “SType”, “NumberOfStates”, “VertexTypeOfSource”, and “InitialConfiguration”.

<Algorithm>
  ...
  <Site>
    <STYPE> 0 </STYPE>
    <NumberOfStates> 2 </NumberOfStates>
    <LocalStates> -0.5 0.5 </LocalStates>
    <VertexTypeOfSource> 0 </VertexTypeOfSource>
    <InitialConfiguration>
       ...
    </InitialConfiguration>
    <InitialConfiguration>
       ...
    </InitialConfiguration>
  </Site>
  ...
</Algorithm>
Algorithm/Site/SType

The index of site type.

Algorithm/Site/NumberOfStates

The number of states of the site.

Algorithm/Site/LocalStates

Mapping from indices of local states to values of states. For example, the z components of the spin operator in the usual spin case.

Algorithm/Site/VertexTypeOfSource

The index of the vertex to be inserted here.

Algorithm/Site/InitialConfiguration

The process of pair creation/annihilation of worm heads. This has children, “State”, “NumberOfChannels”, and “Channel”

<Algorithm>
  ...
  <Site>
    ...
    <InitialConfiguration>
      <State> 0 </State>
      <NumberOfChannels> 2 </NumberOfChannels>
      <Channel> 0 1 0.5 </Channel>
      <Channel> 1 1 0.5 </Channel>
    </InitialConfiguration>
    ...
  </Site>
  ...
</Algorithm>
Algorithm/Site/InitialConfiguration/State

The state index of the site without worms (before creation or after annihilation).

Algorithm/Site/InitialConfiguration/NumberOfChannels

The number of the channels (result of creation/annihilation).

Algorithm/Site/InitialConfiguration/Channel

Channels. This takes two integers and one floating number.

  • First figure denotes the direction of the worm head ( 0 for negative and 1 for positive in the imaginary time direction).

  • Second figure denotes the state between worms.

  • Third figure denotes the probability of this channel.

If the result has no worm heads, let both the first and the second integers be -1.

Algorithm/Interaction

This defines an interaction. This has children, “IType”, “VType”, “NBody”, “EBase”, “VertexDensity”, and “Sign”.

<Algorithm>
  ...
  <Interaction>
    <IType> 0 </IType>
    <VType> 1 </VType>
    <NBody> 2 </NBody>
    <EBase> 0.125 </EBase>
    <VertexDensity> 0 0 0.25 </VertexDensity>
    <VertexDensity> 1 1 0.25 </VertexDensity>
    <Sign> 0 1 1 0 -1.0 </Sign>
    <Sign> 1 0 0 1 -1.0 </Sign>
  </Interaction>
  ...
</Algorithm>
Algorithm/Interaction/IType

The index of the interaction.

Algorithm/Interaction/VType

The index of the vertex to be inserted.

Algorithm/Interaction/NBody

The number of sites involved in this interaction. An onebody interaction such as the Zeeman term has 1 and a twobody interaction such as the exchange coupling has 2. Three or higher body interaction can be treated.

Algorithm/Interaction/EBase

The offset of the local energy. This value does not contribute to the simulation, but to the value of energy in the final result.

Algorithm/Interaction/VertexDensity

The density of vertex to be inserted. This takes integers as many as “Algorithm/Interaction/NBody” and one preceding floating number. The integers denote the states of sites (the order should be compatible with the order of sites in “I” of the lattice file). The last floating number represents the density.

Algorithm/Interaction/Sign

The sign of the local weight, \(\textrm{Sgn}(\langle f | -\mathcal{H} | i \rangle)\) . This takes integers as many as \(2\times\) “Algorithm/Interaction/NBody” and one preceding floating number. The integers denote the states of sites before and after applying the local Hamiltonian. The last floating number represents the sign. If the sign is equal to \(1.0\):, this element (<Sign> ... </Sign>) can be omitted.

For example, <Sign> 0 1 1 0 -1.0 </Sign> means \(\langle 1 0 | \left(-\mathcal{H}\right) | 0 1 \rangle < 0\).

Algorithm/Vertex

This defines a vertex. This has children, “VType”, “VCategory”, “NBody”, “NumberOfInitialConfigurations”, and “InitialConfiguration”. Vertices belongs to a category specified by “Algorithm/Vertex/VCategory”.

<Algorithm>
  ...
  <Vertex>
    <VTYPE> 0 </VTYPE>
    <VCATEGORY> 1 </VCATEGORY>
    <NBODY> 1 </NBODY>
    <NumberOfInitialConfigurations> 4 </NumberOfInitialConfigurations>
    <InitialConfiguration>
      ...
    </InitialConfiguration>
    ...
    <InitialConfiguration>
      ...
    </InitialConfiguration>
  </Vertex>
  ...
</Algorithm>
Algorithm/Vertex/VType

The index of the vertex.

Algorithm/Vertex/VCategory

  1. Boundary of imaginary time. Users need not define this.

  2. Worm tail.

  3. Interaction.

Algorithm/Vertex/NBody

The number of sites involved.

Algorithm/Vertex/NumberOfInitialConfigurations

The number of initial states.

Algorithm/Vertex/InitialConfiguration

This defines scattering results of a worm head for each initial states. “Algorithm/Vertex” should has this elements as many as the number specified by “Algorithm/Vertex/NumberOfInitialConfigurations”. This has children, “State”, “IncomingDirection”, “NewState”, “NumberOfChannels”, “Channel”.

<Algorithm>
  ...
  <Vertex>
    ...
    <InitialConfiguration>
      <State>  1 0 0 1 </State>
      <IncomingDirection> 0 </IncomingDirection>
      <NewState> 0 </NewState>
      <NumberOfChannels> 1 </NumberOfChannels>
      <Channel>    3    0       1.0000000000000000 </Channel>
    </InitialConfiguration>
    ...
  </Vertex>
  ...
</Algorithm>

This example represents the following scenario;

  • Initial states of bottom-left(0), top-left(0), bottom-right(2), and top-right(3) are 1, 0, 0, and 1, respectively.

  • A worm head comes from bottom-left(0) and changes the state of this leg to 0.

  • The worm head will be scattered to leg(3) and the state of outgoing leg will be changed to 0 with the probability 1.

Algorithm/Vertex/InitialConfiguration/State

The initial states of the legs of the vertex. Since the number of the legs is as twice as the number specified by “Algorithm/Vertex/NBody”, say \(m\), this takes \(2m\) integers. Legs are in the same order as the corresponding sites. For two legs on the same site, the leg with the smaller imaginary time comes first.

Algorithm/Vertex/InitialConfiguration/IncomingDirection

The index of the leg from which a worm head comes.

Algorithm/Vertex/InitialConfiguration/NewState

The state of the “Algorithm/Vertex/InitialConfiguration/IncomingDirection” leg after a worm head comes.

Algorithm/Vertex/InitialConfiguration/NumberOfChannels

The number of scattering channels (final results).

Algorithm/Vertex/InitialConfiguration/Channel

A scattering channel. This takes two integers and one floating number.

  • First figure denotes the index of the leg where the scattered worm head goes out.

  • Second figure denotes the state of the leg where the scattered worm head goes out after the scattering.

  • Last figure denotes the probability of this channel.

For the special case, the pair-annihilation of worm heads, let both the first and the second integer be -1.

4.3.5. Wavevector XML file wavevector.xml

A wavevector XML file is a textfile written in a XML-like format. This defines the wavevectors to calculate several observables: staggered magnetization

\[M^{z}(\vec{k}) \equiv \frac{1}{N} \sum_i e^{-i\vec{k}\vec\vec{r}_i} \left\langle M^{z}_i \right\rangle,\]

dynamical structure factor

\[S^{zz}(\vec{k},\tau) \equiv \left\langle M^z(\vec{k},\tau)M^z(-\vec{k},0) \right\rangle - \left\langle M^z(\vec{k},\tau)\right\rangle \left\langle M^z(-\vec{k},0)\right\rangle ,\]

and momentum space temperature Green’s function

\[G(\vec{k},\tau) \equiv \left\langle M^+(\vec{k}, \tau) M^-(-\vec{k},0) \right\rangle .\]

This can be generated from a wavevector datafile via dla_alg.

A structure factor file has only one element, “WaveVector”, and the other elements are children of this.

WaveVector

The root element. This has children, “Comment”, “NumberOfSites”, “NumberOfWaveVectors” and “RK”.

WaveVector/Comment

(Optional) Comment. DSQSS ignores this.

WaveVector/NumberOfSites

The number of lattice sites.

WaveVector/NumberOfWaveVectors

The number of Wavevectors \(\vec{k}\).

WaveVector/RK

The phase factor \(z = \exp{\vec{r}\cdot\vec{k}}\) for a pair of a wave vector and a site. This takes four figures, “\(\mathrm{Re}z\)”, “\(\mathrm{Im}z\)”, “the index of the site”, “the index of the wave vector”. “StructureFactor” should has this elements as many as the number specified by “StructureFactor/NumberOfElements”.

4.3.6. Relative coordinate XML file displacement.xml

A relative coordinate XML file is a textfile written in a XML-like format. This defines relative coordinate between two sites, \(\vec{r}_{ij}\), to calculate real space temperature Green’s function,

\[G(\vec{r}_{ij},\tau) \equiv \left\langle M_i^+(\tau) M_j^- \right\rangle .\]

This file can be generated by using dla_alg.

A relative coordinate XML file has only one element, “Displacements”, and the other elements belong to this as children.

Displacements

The root element. This has children, “Comment”, “NumberOfKinds”, “NumberOfSites”, and “R”.

Displacements/Comment

(Optional) Comment. DSQSS ignores this.

Displacements/NumberOfSites

The number of lattice sites.

Displacements/NumberOfKinds

The number of relative coordinates.

Displacements/R

This takes three integers, “the index of the relative coordinate”, “the index of the site \(i\)”, and “the index of the site \(j\)”. “CorrelationFunction” should has this elements as many as the number specified by “CorrelationFunction/NumberOfKinds”.