4.2.3. ModPara file¶
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Model_Parameters 0
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VMC_Cal_Parameters
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CDataFileHead zvo
CParaFileHead zqp
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Nsite 16
Ncond 16
2Sz 0
Lanczos_max 1000
initial_iv 12
exct 1
LanczosEps 14
LanczosTarget 2
LargeValue 12
NumAve 5
ExpecInterval 20
File format¶
Lines 1-4: Header
Line 6: [string01] [string02]
Lines 7-8: Header
Lines 9- : [string01] [int01].
Parameters¶
[string01]
Type : String
Description : Select a word from keywords.
[string02]
Type : String (a blank parameter is not allowed)
Description : Set a header for output files.
[int01]
Type : Int (a blank parameter is not allowed)
Description : A parameter that is correlated with a keyword.
Use rules¶
From Line 9: After setting keywords at [string 01], a half-width blank is needed for setting a parameter
All the parameters are needed and the order for the parameters is fixed
Keywords and parameters¶
In the following, common parameters and parameters for each method are shown.
Common parameters¶
CDataFileHeadType : String (a blank parameter is not allowed)
Description : A header for output files. For example, the output filename for one-body Green’s function becomes “xxx_Lanczos_cisajs.dat” (xxx are the characters set by
CDataFileHead).NsiteType : Int (positive integer)
Description : The number of sites.
NcondType : Int (positive integer)
Description : The number of conduction electrons (not used in grand canonical ensemble).
2SzType : Int (positive integer)
Description : The total value of \(2S_z\) (not used in grand canonical ensemble). For conservation of \(S_z\) in the case of
CalcModel= 0 (fermion Hubbard model) or 2 (Kondo lattice model), setNcond.initial_ivType : Int
Description : An initial vector is specified with this parameter.
Lanczos method
For canonical ensemble and
initial_iv\(\geq 0\)The non-zero components of an initial vector are specified with this parameter.
For grand canonical ensemble or
initial_iv\(< 0\)The seed of the random generator is given by this parameter and the random vector is used as the initial vector.
TPQ method
The seed of the random generator is given by this parameter and the random vector is used as the initial vector.
See Algorithm for details of setting an initial vector.
CalcHSType : Int (positive integer)
Description : If
CalcHS=1, an efficient algorithm for generating the restricted Hilbert space with the specified quantum number is used (Details of algorithm is shown in http://www.pasums.issp.u-tokyo.ac.jp/wp-content/themes/HPhi/media/develop/tips.pdf [in Japanese]). Default value is 1 and the efficient algorithm is used.
Lanczos method¶
Lanczos_maxType : Int (positive integer)
Description : The maximum number of Lanczos steps in the calculation. When the convergence within the specified accuracy is satisfied, the calculation is completed before a step reaches
Lanczos_max. In the case of restart calculation,Lanczos_maxmust be larger than that of the previous calculation.exctType : Int (positive integer)
Description : An integer for setting the number of eigenvectors obtained from the ground energy by the Lanczos method.
LanczosEpsType : Int (positive integer)
Description : An integer for judging the convergence of the Lanczos method. The convergence is determined by whether the condition is satisfied that the relative error between an eigenvalue and an eigenvalue at the Lanczos step of the one step before is less than \(10^{- \verb|LanczosEps|}\).
LanczosTargetType : Int (positive integer)
Description : An integer giving the target of the eigenvalue for judging the convergence of the Lanczos method. For example, the target becomes a ground state when
LanczosTargetis equal to one, and a first excited state whenLanczosTargetis equal to two.
CG method¶
exctType : Int (positive integer)
Description : The number of eigenvectors is specified.
Lanczos_maxType : Int (positive integer)
Description : The maximum number of iteration steps in the calculation. When the convergence within the specified accuracy is satisfied, the calculation is completed before a step reaches
Lanczos_max. In the case of restart calculation,Lanczos_maxmust be larger than that of the previous calculation.LanczosEpsType : Int (positive integer)
Description : For
method="CG", the calculation finishes when the 2-norm of the residual vector becomes smaller than \(10^{- \verb|LanczosEps|/2}\).
TPQ (mTPQ/cTPQ) method¶
Lanczos_maxType : Int (positive integer)
Description : The total number of TPQ steps is specified with this parameter. In the case of restart calculation,
Lanczos_maxmust be larger than that of the previous calculation.LargeValueType : Double
Description : An integer giving \(l\) of \(l-{\mathcal H}/N_{s}\) used in the mTPQ method. In the cTPQ method, \(l\) is used as the width of the imaginary-time evolution, i.e., \(\Delta\tau=1/l\). See Algorithm for the details of the cTPQ method.
NumAveType : Int
Description : An integer giving the number of independent runs for the TPQ method.
ExpecIntervalType : Int
Description : An integer giving the interval steps of calculating the correlation functions in the TPQ method.Note: A small interval increases the time cost of calculations.ExpandCoefType : Int (positive integer)
Description : An integer giving the expansion order \(n_{\rm max}\) for cTPQ method;
(4.5)¶\[U(\Delta\tau) = \sum_{n=0}^{n_{\rm max}}\frac{1}{n!}\left(-\frac{\Delta\tau}{2}\mathcal{H}\right)^n .\]See Algorithm for the details of the cTPQ method.
Calculating dynamical Green’s functions¶
OmegaOrgType : Complex
Description : The center value of the frequency. Specify the real and imaginary parts in that order separated by a space, and if there is no imaginary part, the real part of the frequency is only given.
OmegaImType : Double
Description : The imaginary part of the frequency. When
OmegaOrgis defined in amodparafile,OmegaImis added to the imaginary value ofOmegaOrg.OmegaMinType : Complex
Description : The lower limit of the frequency from
OmegaOrg. Specify the real and imaginary parts in that order separated by a space, and if there is no imaginary part, the real part of the frequency is only given.OmegaMaxType : Complex
Description : The upper limit of the frequency from
OmegaOrg. Specify the real and imaginary parts in that order separated by a space, and if there is no imaginary part, a real part of the frequency is only given.NOmegaType : Int
Description : The integer for defining the step size of the frequency \(\Delta \omega = (\)
OmegaMax-OmegaMin\()/N_{\omega}\). The frequency is given by \(z_n=\)OmegaOrg\(+\)OmegaMin\(+ \Delta \omega \times n\).
Real time evolution method¶
Lanczos_maxType : Int (positive integer)
Description : The total number of real time evolution steps is specified with this parameter. In the case of restart calculation,
Lanczos_maxmust be larger than that of the previous calculation.ExpandCoefType : Int (positive integer)
Description : An integer giving the expansion order \(n\) for real-time evolution method;
(4.6)¶\[\exp\left(-i \mathcal{H} \Delta t \right) = \sum_{i=0}^{N}\frac{1}{n!}\left(-i \mathcal{H} \Delta t \right)^n.\]ExpecIntervalType : Int (positive integer)
Description : An integer giving the interval steps of calculating the correlation functions.Note: A small interval increases the time cost of calculations.OutputIntervalType : Int (positive integer)
Description : An integer giving the interval steps of output the wave function.The wave vector is output whenOutputEigenVec=1inCalcModfile.
