5.1. Input files for DSQSS/DLA

5.1.1. The list of input files

qmc.inp	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).
sf.xml	Indication of wave vectors for structure factors. (optional)
cf.xml	Indexing directions between all the sites. (optional)

5.1.2. Parameter file qmc.inp

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. Overwrite a setting in lattice.xml.
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.
sfinpfile	string	–	A structure factor file. If it is an empty string, structure factors will not be calculated.
cfinpfile	string	–	A real space temperature Green’s function file. If it is an empty string, real space temperature Green’s functions will not be calculated.
ckinpfile	string	–	A momentum space temperature Green’s function file. If it is an empty string, momentum space temperature Green’s functions 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.
runtype	int	0	Method. This remains for backward compatibility.

• 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.

5.1.3. Lattice file lattice.xml

A lattice file is a textfile written in XML format. This defines timespace to be simulation, for example, the number of sites, the connections between sites, the inverse temperature, and so on. This file can be very complicated, so DSQSS has a utility tool lattgene to generate lattice files describing common lattices, such as a hypercubic lattice.

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/Beta

The inverse temperature. This is overwritten by the parameter file.

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/NumberOfCells

The number of unitcells.

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/BondDimension

Parameter for the winding number.

Lattice/NumberOfEdgeInteractions

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

Lattice/S

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

<S> 3 0 1 </S>
# the site with index 3 has the site type of 0 and the measure type of 1.

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.

5.1.4. Algorithm 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

User can use this value for user’s own purpose in “measure_specific.cc”. In the original “measure_specific.cc” uses this value as 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>
    <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/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”, and “VertexDensity”.

<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>
  </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/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

0. Boundary of imaginary time. Users need not define this.
1. Worm tail.
2. 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.

5.1.5. Hamiltonian file hamiltonian.xml

A Hamiltonian file is a textfile written in XML format. This defines the local Hamiltonians, e.g., a bond Hamiltonian. This file is used as an input of dla_alg in order to generate algorithm.xml . DSQSS has utility tools hamgen_H and hamgen_B to generate hamiltonian files describing the Heisenberg spin model and the Bose-Hubbard model.

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

Hamiltonian

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

Hamiltonian/General

General parameters such as the number of site types. This has children, “NSTYPE”, “NITYPE”, “NXMAX”, and “Comment”.

<Hamiltonian>
   <General>
     <Comment> SU(2) Heisenberg model with S=1/2 </Comment>
     <NSTYPE> 1 </NSTYPE>
     <NITYPE> 1 </NITYPE>
     <NXMAX>  2 </NXMAX>
   </General>
  ...
</Hamiltonian>

Hamiltonian/General/Comment

(Optional) Comment. DSQSS ignores this.

Hamiltonian/General/NSTYPE

The number of site types.

Hamiltonian/General/NITYPE

The number of interaction types.

Hamiltonian/General/NXMAX

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

Hamiltonian/Site

This defines a site type, for example, the number of states. This has children “STYPE”, “TTYPE”, and “NX”.

<Hamiltonian>
  ...
  <Site>
    <STYPE> 0 </STYPE>
    <TTYPE> 0 </TTYPE>
    <NX>   2 </NX>
  </Site>
  ...
</Hamiltonian>

Hamiltonian/Site/STYPE

The index of site type.

Hamiltonian/Site/TTYPE

The index of the source type (type of pair creation/annihilation of worm-heads.)

Hamiltonian/Site/NX

The number of states of the site.

Hamiltonian/Source

This defines a source type, that is, the pair-creation/annihilation of worm-heads. This has children “TTYPE”, “STYPE”, and “Weight”.

<Source>
  <TTYPE> 0 </TTYPE>
  <STYPE> 0 </STYPE>
  <Weight> 0 1       0.5000000000000000 </Weight>
  <Weight> 1 0       0.5000000000000000 </Weight>
</Source>

Hamiltonian/Source/TTYPE

The index of the source type.

Hamiltonian/Source/STYPE

The index of the site type.

Hamiltonian/Source/Weight

The weight of the creation/annihilation operator. This takes two integers and one floating number. The integers denote the states of the site before and after applying the operator, respectively. The floating number denotes the matrix element.

For example, 0 1 0.5 means \(\langle 1 | \mathcal{H} | 0 \rangle = 0.5\).

Hamiltonian/Interaction

This defines an interaction type. This has children “ITYPE”, “STYPE”, “NBODY”, and “Weight”.

<Hamiltonian>
  ...
  <Interaction>
    <ITYPE> 0 </ITYPE>
    <NBODY> 2 </NBODY>
    <STYPE> 0 0 </STYPE>
    <Weight> 0 0 0 0      -0.2500000000000000 </Weight>
    <Weight> 1 1 0 0       0.2500000000000000 </Weight>
    <Weight> 1 0 0 1       0.5000000000000000 </Weight>
    <Weight> 0 1 1 0       0.5000000000000000 </Weight>
    <Weight> 0 0 1 1       0.2500000000000000 </Weight>
    <Weight> 1 1 1 1      -0.2500000000000000 </Weight>
  </Interaction>
  ...
</Hamiltonian>

Hamiltonian/Interaction/ITYPE

The index of the interaction type.

Hamiltonian/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.

Hamiltonian/Interaction/ITYPE

The indices of sites involved in this interaction. This takes NBODY integers.

Hamiltonian/Interaction/Weight

The matrix elements of the local Hamiltonian.

This takes integers as many as \(2\times\) NBODY and one preceding floating number. The integers denote the states of sites before and after applying the local Hamiltonian. The last floating number denotes the matrix element multiplied by \(-1\). For off-diagonal elements, this value should be positive [1].

For example, 0 0 1 1 0.25 means \(\langle 0 1 | \mathcal{H} | 0 1 \rangle = -0.25\) and 0 1 1 0 0.5 means \(\left| \langle 1 0 | \mathcal{H} | 0 1 \rangle \right| = 0.5\).

5.1.6. Structure factor file sf.xml

A structure factor file is a textfile written in a XML-like format. This defines wave vectors and the discretization of imaginary time to calculate the dynamical structure factor

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

DSQSS has a utility tool to generate a structure factor file, sfgene.

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

StructureFactor

The root element. This has children, “Ntau”, “NumberOfElements”, “CutoffOfNtau”, “NumberOfInverseLattice”, and “SF”.

StructureFactor/Comment

(Optional) Comment. DSQSS ignores this.

StructureFactor/Ntau

The number of discretization of the imaginary time axis.

StructureFactor/CutoffOfNtau

The maximum of the imaginary time distance of the dynamical structure factor, \(\tau\). This takes an integer in \(0, 1, \dots, \mathrm{Ntau}\).

StructureFactor/NumberOfInverseLattice

The number of wave vectors, \(\vec{k}\)

StructureFactor/NumberOfElements

The number of the combination of wave vectors and sites.

StructureFactor/SF

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”.

5.1.7. Real space temperature Green’s function file cf.xml

Real space temperature Green’s function 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,

\[G(\vec{r},\tau) \equiv \frac{1}{N^2}\sum_{i,j}\left\langle M_i^+(\tau) M_j^- \right\rangle \delta(\vec{r}-\vec{r}_{ij}) .\]

More precisely, this groups all the pair of sites by the relative coordinates.

DSQSS has a utility tool to generate a real space temperature Green’s function file, cfgene.

A real space temperature Green’s function file has only one element, “CorrelationFunction”, and the other elements belong to this as children.

CorrelationFunction

The root element. This has children, “Ntau”, “NumberOfKinds”, and “CF”.

CorrelationFunction/Comment

(Optional) Comment. DSQSS ignores this.

CorrelationFunction/Ntau

The number of discretization of the imaginary time axis.

CorrelationFunction/NumberOfKinds

The number of relative coordinates.

CorrelationFunction/CF

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”.

5.1.8. Momentum space temperature Green’s function file ck.xml

A momentum space temperature Green’s function file is a textfile written in a XML-like format. This defines wave vectors and the discretization of imaginary time to calculate the momentum space temperature Green’s function,

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

Since this file has the format as same as that of the structure factor file including the names of elements, users can use the same file.

Footnote

[1]	In other words, we always perform a simulation of the “absolute” system. We plans to implement the negative-sign reweighting and remove this limitation in DSQSS v2.