# Input-file format¶

The input file consists of five parameter blocks named [model], [system], [impurity_solver], [control], and [tool].

The following table shows which blocks are used by each program.

dcore_pre

dcore

dcore_check

dcore_post

[model]

Yes

Yes

Yes

Yes

[system]

Yes

Yes

Yes

[impurity_solver]

Yes

Yes

[control]

Yes

[tool]

Yes

Yes

[mpi]

Yes

Yes

For example, we can see that dcore_pre needs to be re-executed only when [model] block is changed.

The parameters included in each block are explained below.

## [model] block¶

This block includes parameters for defining a model to be solved.

Name

Type

Default

Description

seedname

String

dcore

Name of the system. The model HDF5 file will be seedname.h5.

lattice

String

chain

Chosen from “chain”, “square”, “cubic”, “bethe”, “wannier90”, and “external”

t

Float

1.0

Transfer integral (Nearest neighbor)

t’

Float

0.0

Transfer integral (Second nearest)

nelec

Float

1.0

Number of electrons per unit cell.

norb

String

1

Number of orbitals at each correlated shell (ncor integers separated by commas or spaces.)

ncor

Integer

1

Number of correlated shells in a unit cell (for lattice = wannier90).

corr_to_inequiv

String

None

Mapping from correlated shells to equivalent shells (for lattice = wannier90)

bvec

String

[(1.0,0.0,0.0),(0.0,1.0,0.0),(0.0,0.0,1.0)]

Reciprocal lattice vectors in arbitrary unit.

nk

Integer

8

Number of k along each line

nk0

Integer

0

Number of k along b_0 (for lattice = wannier90, external)

nk1

Integer

0

Number of k along b_1 (for lattice = wannier90, external)

nk2

Integer

0

Number of k along b_2 (for lattice = wannier90, external)

spin_orbit

Bool

False

Whether the spin-orbit case.

interaction

String

kanamori

Chosen from “slater_uj”, “slater_f”, “kanamori”, “respack” (See below)

density_density

Bool

False

If true, only the density-density part of the interaction is used (See below).

kanamori

String

None

U (Diagonal Coulomb pot.), U’ (Off-diagonal Coulomb pot.) and J (Hund coupling) (See below).

slater_f

String

None

Angular momentum, Slater integrals F (See below).

slater_uj

String

None

Angular momentum, Slater integrals in U and J (See below).

local_potential_matrix

String

None

dict of {ish: ‘filename’} to specify local potential matrix of ish-th shell

local_potential_factor

String

1.0

Prefactors to the local potential matrix (float or list with len=ncor)

### lattice¶

For model calculations, the following preset models are defined:

• chain

• square

• cubic

• bethe (semicircular DOS with energy ranges [-2t:2t])

For DFT+DMFT calculations, hopping parameters in the Wannier90 format can be imported by

• wannier90

Place the Wannier90 file in the current directory with the name seedname_hr.dat.

For experts, the lattice data may be prepared by your own. In this case, use

• external

In this mode, you should make all necessary data in dft_input group of seedname.h5. The data structure follows DFTTools. For details, see the reference manual of DFTTools.

The pre-process dcore_pre does not touch the data in dft_input group, and write only additional data such as interactions into DCore group.

### interaction¶

Model Hamiltonian is defined as

${\hat H} = \sum_{i j} \sum_{\alpha \beta}^{N_{\rm band}} \sum_{\sigma=\uparrow, \downarrow} t_{i \alpha j \beta} c_{i \alpha \sigma}^\dagger c_{j \beta \sigma} +h.c. + {\hat H}_{\rm int},$

where

${\hat H}_{\rm int} = \frac{1}{2} \sum_{i, \alpha \beta \gamma \delta,\sigma \sigma'} U^{i}_{\alpha \beta \gamma \delta} c_{i \alpha \sigma}^\dagger c_{i \beta \sigma'}^\dagger c_{i \delta \sigma'} c_{i \gamma \sigma}.$

The interaction matrix $$U^{i}_{\alpha \beta \gamma \delta}$$ is specified by the parameter interaction.

• If interaction = kanamori

In this case, the Kanamori-type interaction is used, i.e.

\begin{split}\begin{align} U_{\alpha \alpha \alpha \alpha} &= U, \\ U_{\alpha \beta \alpha \beta} &= U' \qquad (\alpha \neq \beta), \\ U_{\alpha \beta \beta \alpha} &= J \qquad (\alpha \neq \beta), \\ U_{\alpha \alpha \beta \beta} &= J \qquad (\alpha \neq \beta), \end{align}\end{split}

where $$U, U', J$$ at each correlated shell are specified by the parameter kanamori as

interaction = kanamori
kanamori = [(U_1, U'_1, J_1), (U_2, U'_2, J_2), ... ]


For example, if there are two correlated shells that have $$(U, U', J) = (4, 2, 1)$$ and $$(U, U', J) = (6, 3, 1.5)$$, respectively, you need to set the input parameters as

interaction = kanamori
kanamori = [(4.0, 2.0, 1.0), (6.0, 3.0, 1.5)]

• If interaction = slater_f

In this case, the interaction matrix is constructed by the effective Slater integrals $$F_0, F_2, F_4, F_6$$. These Slater integrals and the angular momentum at each correlated shell are specified by the parameter slater_f as follows

interaction = slater_f
slater_f = [(angular_momentum, F_0, F_2, F_4, F_6), ... ]


For example, if there are two correlated shells, one has d-orbital with $$(F_0, F_2, F_4) = (2, 1, 0.5)$$ and the other has p-orbital with $$(F_0, F_2) = (3, 1.5)$$, you need to set the input parameter as

interaction = slater_f
slater_f = [(2, 2.0, 1.0, 0.5, 0.0), (1, 3.0, 1.5 0.0, 0.0)]


Note

You must specify all of $$F_0, F_2, F_4, F_6$$.

• If interaction = slater_uj

In this case, the Slater-type interaction is used. The effective Slater integrals are computed with the following formulae:

• $$l = 1$$

$F_0 = U, \quad F_2 = 5 J$
• $$l=2$$

$F_0 = U, \quad F_2 = \frac{14 J}{1.0 + 0.63},\quad F_4 = 0.63 F_2$
• $$l=3$$

$F_0 = U, \quad F_2 = \frac{6435 J}{286 + 195 \times 451 / 675 + 250 \times 1001 / 2025},\quad F_4 = \frac{451 F_2}{675},\quad F_6 = \frac{1001 F_2}{2025}$

The $$U$$, $$J$$ and the angular momentum at each correlated shell are specified by the parameter slater_uj as

interaction = slater_uj
slater_uj = [(angular_momentum1, U1, J1), (angular_momentum2, U2, J2), ... ]

• If interaction = respack

Use the output by RESPACK. Under construction.

If you want to treat only the density-density part

${\hat H}_{\rm int} = \frac{1}{2} \sum_{i, \alpha, \sigma \sigma'} U^{i}_{\alpha \alpha \alpha \alpha} c_{i \alpha \sigma}^\dagger c_{i \beta \sigma'}^\dagger c_{i \beta \sigma'} c_{i \alpha \sigma} + \frac{1}{2} \sum_{i, \alpha \neq \beta, \sigma \sigma'} U^{i}_{\alpha \beta \alpha \beta} c_{i \alpha \sigma}^\dagger c_{i \beta \sigma'}^\dagger c_{i \beta \sigma'} c_{i \alpha \sigma} + \frac{1}{2} \sum_{i, \alpha \neq \beta, \sigma} U^{i}_{\alpha \beta \beta \alpha} c_{i \alpha \sigma}^\dagger c_{i \beta \sigma}^\dagger c_{i \alpha \sigma} c_{i \beta \sigma},$

you specify the parameter density_density as

density_density = True


Note

It can not be used in conjunction to the Hubbard-I solver or the double-counting correction.

### local potential¶

An arbitrary local potential can be implemented using parameters local_potential_*. The format looks like

[model]
local_potential_matrix = {0: 'pot0.txt', 1: 'pot1.txt'}
local_potential_factor = 0.01


Here, local_potential_matrix describes, in the python dictionary format, a set of the inequivalent shell index ish and the filename which defines the local potential matrix. The parameter local_potential_factor defines a prefactor to the potential matrix.

For example, the Zeeman term along z-axis for S=1/2 is represented by

\$ cat pot0.txt
# spin orb1 orb2  Re Im
0 0 0   0.5 0.
1 0 0  -0.5 0.


and the magnetic field is specified by local_potential_factor.

## [system] block¶

This block includes thermodynamic parameters and some technical parameters such as the number of Matsubara frequencies.

Name

Type

Default

Description

beta

Float

1.0

Inverse temperature. This parameter is overridden, if T is given.

T

Float

-1.0

Temperature. If this parameter is given, beta is overridden by 1/T.

n_iw

Integer

2048

Number of Matsubara frequencies

fix_mu

Bool

False

Whether or not to fix chemical potential to a given value.

mu

Float

0.0

Initial chemical potential.

prec_mu

Float

0.0001

Threshold for calculating chemical potential with the bisection method.

with_dc

Bool

False

Whether or not use double-counting correction (See below)

dc_type

String

HF_DFT

Chosen from ‘HF_DFT’ (default), ‘HF_imp’, ‘FLL’

If the parameter with_dc is specified to True, the following part of the self-energy is subtracted to avoid the double-counting error of the self-energy.

$\Sigma_{i, \alpha \sigma \beta \sigma'}^{\rm dc-imp} = \delta_{\sigma \sigma'} \sum_{\gamma \delta \sigma_1} U_{\alpha \gamma \beta \delta} \langle c_{\gamma \sigma_1}^\dagger c_{\delta \sigma_1}\rangle_0 - \sum_{\gamma \delta} U_{\alpha \gamma \delta \beta} \langle c_{\gamma \sigma'}^\dagger c_{\delta \sigma}\rangle_0,$

where $$\langle \cdots \rangle_0$$ indicates the expectation value at the initial (Kohn-Sham) state.

## [impurity_solver] block¶

This block specifies an impurity solver to be used and necessary parameters for running the solver program.

Name

Type

Default

Description

name

String

null

Name of impurity solver. Available options are null, TRIQS/cthyb, TRIQS/hubbard-I, ALPS/cthyb, ALPS/cthyb-seg, pomerol.

basis_rotation

String

None

You can specify either ‘Hloc’, ‘None’, or the location of a file..

Additionally, we have to specify solver-dependent parameters in the way like n_cycles{int} = 500000. For details, see the reference manual for each solver.

## [control] block¶

This block includes parameters that control the self-consistency loop of DMFT.

Name

Type

Default

Description

max_step

Integer

100

Maximum steps of DMFT loops

sigma_mix

Float

0.5

Mixing parameter for self-energy

restart

Bool

False

Whether or not restart from a previous calculation stored in a HDF file.

initial_static_self_energy

String

None

dict of {ish: ‘filename’} to specify initial value of the self-energy of ish-th shell. The file format is the same as local_potential_matrix.

initial_self_energy

String

None

Filename containing initial self-energy in the same format as sigma.dat generated by dcore_check.

time_reversal

Bool

False

If true, an average over spin components are taken.

symmetry_generators

String

None

Generators for symmetrization of self-energy.

n_converge

Integer

1

The DMFT loop is terminated if the convergence criterion defined with converge_tol is satisfied n_converge times consecutively.

converge_tol

Float

0.0

Tolerance in the convergence check. The chemical potential and the renormalization factor are examined.

## [tool] block¶

This block includes parameters that are solely used by dcore_post.

Name

Type

Default

Description

nnode

Integer

0

[NOT USED] Number of node for the k path

nk_line

Integer

8

Number of k along each line

knode

String

[(G,0.0,0.0,0.0),(X,1.0,0.0,0.0)]

The name and the fractional coordinate of each k-node.

omega_min

Float

-1.0

Minimum value of real frequency

omega_max

Float

1.0

Max value of real frequency

Nomega

Integer

100

Number of real frequencies

Float

0.0

eta

Float

0.0

Imaginary frequency shift for the Pade approximation

Float

1e+20

Integer

20

Minimum number of Matsubara frequencies used for Pade approximation.

Integer

-1

Maximum number of Matsubara frequencies used for Pade approximation. If negative, this will be replaced with n_iw in [system] block.

omega_check

Float

0.0

Maximum frequency for dcore_check. If not specified, a fixed number of Matsubara points are taken.

nk_mesh

Integer

0

Number of k points along each axis for computation of A(k,omega) on a 3D mesh

nk0_mesh

Integer

0

Number of k points along b_0 for computation of A(k,omega) on a 3D mesh

nk1_mesh

Integer

0

Number of k points along b_1 for computation of A(k,omega) on a 3D mesh

nk2_mesh

Integer

0

Number of k points along b_2 for computation of A(k,omega) on a 3D mesh

## [mpi] block¶

This block includes parameters which are read by dcore and dcore_post.

Name

Type

Default

Description

command

String

mpirun -np #

Command for executing a MPI job. # will be relaced by the number of processes.

When an option -DMPIEXEC=<MPIRUN> is passed to the cmake command, The default value of command will be replaced with <MPIRUN>.