Input parameters for Standard modeΒΆ
We show the following example of the input file.
model = "Hubbard"
lattice = "wannier90"
a0w = 2
a0l = 0
a0h = 2
a1w = 0
a1l = 2
a1h = 2
a2w = 1
a2l = 0
a2h = 0
2Sz = 0
nelec = 4
cutoff_t = 0.1
cutoff_u = 1.0
cutoff_j = 0.1
The input parameters for the Standard mode to perform calculation of the downfolded model are as follows:
lattice
lattice = "wannier90"
Parameters related to the lattice
W,L,HeightType : int
Description : The alignment of original unit cells is specified.
a0W,a0L,a0H,a1W,a1L,a1H,a2W,a2L,a2HType : int
Description : Three vectors (\({\vec a}_0, {\vec a}_1, {\vec a}_2\)) that specify the lattice . These vectors should be written in the Fractional coordinates of the original transrational vectors.
Wsub,Lsub,HsubType : int (positive). In the default setting,
Wsub=W,Lsub=L,Hsub=Height. Namely, there is no sublattice.Description : They are available only in mVMC. By using these parameters, we can force the pair-orbital symmetrical to the translation of the sublattice. If the sublattice is incommensurate with the original lattice,
vmcdry.outstops.a0Wsub,a0Lsub,a0Hsub,a1Wsub,a1Lsub,a1Hsub,a2Wsub,a2Lsub,a2HsubType : int (positive). In the default setting,
a0Wsub=a0W,a0Lsub=a0L,a0Hsub=a0H,a1Wsub=a1W,a1Lsub=a1L,a1Hsub=a1H,a2Wsub=a2W,a2Lsub=a2L,a2Hsub=a2H. Namely, there is no sublattice.Description : The manner to set these aparameters is same as that for
a0W,a0L,a0H,a1W,a1L,a1H,a2W,a2L,a2H. If the sublattice is incommensurate with the original lattice,vmcdry.outstops.
Parameters related to interactions
lambda_uType : float (greater than or equal to 0)
Default :
1.0Description : A parameter to tune the strength of Coulomb interactions by multiplying :math: lambda_u by them.
lambda_jType : float (greater than or equal to 0)
Default :
1.0Description : A parameter to tune the strength of exchange Coulomb interactions by multiplying :math: lambda_j by them.
lambdaType : float (greater than or equal to 0)
Default :
1.0Description : A parameter to tune the strength of Coulomb and exchange interactions by multiplying :math: lambda by them. When \(\lambda_U\) , \(\lambda_J\) are specified, these settings are used.
cutoff_t,cutoff_u,cutoff_jType : float
Default :
1.0e-8Description : The cutoff parameters for the hopping, Coulomb, exchange integrals. We ignore these integrals smaller than cutoff values.
cutoff_tW,cutoff_tL,cutoff_tHcutoff_UW,cutoff_UL,cutoff_UHcutoff_JW,cutoff_JL,cutoff_JHType :
Default :
cutoff_tW = int((W-1)/2),cutoff_tL=int((L-1)/2),cutoff_tH=int((Height-1)/2)(whenW,LandHeightare not defined, the values are set to 0) and others are set to0.Description : The cutoff parameters for the hopping, Coulomb, exchange integrals. We ignore these integrals that have lattice vector \({\bf R}\) larger than these values.
cutoff_length_t,cutoff_length_U,cutoff_length_JType : float
Default :
cutoff_length_t = -1.0(include all terms), others are set to0.3.Description
The cutoff parameters for the hopping, Coulomb, exchange integrals. We ignore these integrals whose distances are longer than these values. The distances are computed from the position of the Wannier center and unit lattice vectors.
Parameters for one body correction
To avoid double countings in analyzing the lattice model, one body correction is done by subtracting the following terms from one body terms:
\[\begin{split}\begin{aligned} t_{mm}^{\rm DC}({\bf 0}) &\equiv \alpha U_{mm}({\bf 0}) D_{mm}({\bf 0}) + \sum_{({\bf R}, n) \neq ({\bf 0}, m)} U_{m n} ({\bf R})D_{nn}({\bf 0})\\ & - (1-\alpha) \sum_{({\bf R}, n) \neq ({\bf 0}, 0)} J_{m n}({\bf R}) D_{nn}({\bf R}),\\ t_{mn}^{\rm DC}({\bf R}_{ij}) &\equiv \frac{1}{2} J_{mn}({\bf R}_{ij}) \left(D_{nm}({\bf R}_{ji}) + 2 {\rm Re} [D_{nm}({\bf R}_{ji})]\right)\\ &-\frac{1}{2} U_{mn}({\bf R}_{ij}) D_{nm}({\bf R}_{ji}), \quad ({\bf R}_{ij}, m) \neq ({\bf 0}, n), \\ D_{mn}({\bf R}_{ij}) &\equiv \sum_{\sigma} \left\langle c_{im \sigma}^{\dagger} c_{jn \sigma}\right\rangle_{\rm KS}, \end{aligned}\end{split}\]where, the first and second terms correspond to the Hartree and Fock corrections, respectively. \(\alpha\) is a tuning parameter for one body correction from the on-site Coulomb interactions.
doublecountingType : char
Default :
noneDescription :
none: One body correction is not considered.Hartree_U: Hartree correction only considered the contribution from Coulomb interactions \(U_{Rii}\) .Hartree: Hartree correction.full: One body correction including Fock correction. Charge densities \(D_{Rij}\) are obtained by[CDataFileHead]_dr.datwhich is automatically outputted by RESPACK. It is noted that the charge densities are assumed not to depend on spin components.alphaType : float
Default :
0.5Description :
A tuning parameter for one body correction from the on-site Coulomb interactions (\(0\le \alpha \le 1\)).
