8.3. Input parameters for Standard mode¶
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
method = "CG"
2Sz = 0
nelec = 4
exct = 1
cutoff_t = 0.2
cutoff_u = 0.4
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
,Height
Type : int
Description : The alignment of original unit cells is specified.
a0W
,a0L
,a0H
,a1W
,a1L
,a1H
,a2W
,a2L
,a2H
Type : 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
,Hsub
Type : 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.out
stops.a0Wsub
,a0Lsub
,a0Hsub
,a1Wsub
,a1Lsub
,a1Hsub
,a2Wsub
,a2Lsub
,a2Hsub
Type : 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.out
stops.
Parameters related to interactions
lambda_u
Type : float (greater than or equal to 0)
Default :
1.0
Description : A parameter to tune the strength of Coulomb interactions by multiplying :math: lambda_u by them.
lambda_j
Type : float (greater than or equal to 0)
Default :
1.0
Description : A parameter to tune the strength of exchange Coulomb interactions by multiplying :math: lambda_j by them.
lambda
Type : float (greater than or equal to 0)
Default :
1.0
Description : 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_j
Type : float
Default :
1.0e-8
Description : The cutoff parameters for the hopping, Coulomb, exchange integrals. We ignore these integrals smaller than cutoff values.
cutoff_tW
,cutoff_tL
,cutoff_tH
cutoff_UW
,cutoff_UL
,cutoff_UH
cutoff_JW
,cutoff_JL
,cutoff_JH
Type :
Default :
cutoff_tW = int((W-1)/2)
,cutoff_tL=int((L-1)/2)
,cutoff_tH=int((Height-1)/2)
(whenW
,L
andHeight
are 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_J
Type : 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:
(8.6)¶\[\begin{split}\begin{aligned} t_{mm}^{\rm DC}({\bf 0}) &\equiv \alpha U_{mm}({\bf 0}) D_{mm}({\bf 0}) + \sum_{({\bf R}, n) \neq ({\bf 0}, m)} U_{m n} ({\bf R})D_{nn}({\bf 0})\\ & - (1-\alpha) \sum_{({\bf R}, n) \neq ({\bf 0}, 0)} J_{m n}({\bf R}) D_{nn}({\bf R}),\\ t_{mn}^{\rm DC}({\bf R}_{ij}) &\equiv \frac{1}{2} J_{mn}({\bf R}_{ij}) \left(D_{nm}({\bf R}_{ji}) + 2 {\rm Re} [D_{nm}({\bf R}_{ji})]\right)\\ &-\frac{1}{2} U_{mn}({\bf R}_{ij}) D_{nm}({\bf R}_{ji}), \quad ({\bf R}_{ij}, m) \neq ({\bf 0}, n), \\ D_{mn}({\bf R}_{ij}) &\equiv \sum_{\sigma} \left\langle c_{im \sigma}^{\dagger} c_{jn \sigma}\right\rangle_{\rm KS}, \end{aligned}\end{split}\]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.
doublecounting
Type : char
Default :
none
Description :
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.dat
which is automatically outputted by RESPACK. It is noted that the charge densities are assumed not to depend on spin components.alpha
Type : float
Default :
0.5
Description :
A tuning parameter for one body correction from the on-site Coulomb interactions (\(0\le \alpha \le 1\)).