8.3. Input parameters for Standard mode

We show the following example of the input file.

stan.in

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) (when W , L and Height are not defined, the values are set to 0) and others are set to 0.

      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 to 0.3.

      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 (\(0\le \alpha \le 1\)).