Examples

This section provides complete working examples for different use cases.

Hubbard Model (Default)

This example demonstrates a basic Hubbard model on a 2x2 square lattice using the standard lattice definition. This is the recommended starting point.

Source: samples/hubbard/default_model/

Input File

Create stan.in:

model = "Hubbard"
lattice = square
W = 2
L = 2
method = "CG"
2Sz = 0
nelec = 4
exct = 1
t = 1
U = 1

Parameter Explanation

Parameter	Value	Description
model	Hubbard	Hubbard model with hopping and on-site interaction
lattice	square	2D square lattice
W	2	Width: 2 sites in the W direction
L	2	Length: 2 sites in the L direction
method	CG	Conjugate gradient method (solver-specific)
2Sz	0	Total spin projection (2 * Sz = 0)
nelec	4	Number of electrons (half-filling for 4 sites)
exct	1	Number of excited states (solver-specific)
t	1	Nearest-neighbor hopping amplitude
U	1	On-site Coulomb interaction strength

Running the Example

cd samples/hubbard/default_model
../../../build/hphi_dry.out stan.in

Replace hphi_dry.out with the appropriate executable for your target solver.

Expected Behavior

StdFace reads the input file, constructs a 2x2 square lattice Hubbard model, and generates solver input files in the current directory. The specific output files depend on the solver mode used.

Hubbard Model (Wannier90-based)

This advanced example demonstrates importing a tight-binding model from Wannier90 format files. This approach is useful when you have an existing Wannier90 tight-binding Hamiltonian.

Source: samples/hubbard/wannier/

Required Files

This example requires multiple input files:

1. stan.in - Main StdFace input file

2. zvo_geom.dat - Geometry data (lattice vectors and atomic positions)

3. zvo_hr.dat - Hopping parameters in Wannier90 format

4. zvo_ur.dat - On-site interaction parameters in Wannier90 format

Main Input File (stan.in)

model = "Hubbard"
lattice = "wannier90"
W = 2
L = 2
method = "CG"
2Sz = 0
nelec = 4
exct = 1

Key difference from the default example: lattice = "wannier90" instructs StdFace to read lattice and hopping information from Wannier90 format files instead of using built-in lattice constructors.

Geometry File (zvo_geom.dat)

This file defines the lattice vectors and atomic positions:

1.0000000000   0.0000000000   0.0000000000
0.0000000000   1.0000000000   0.0000000000
0.0000000000   0.0000000000   1.0000000000
1
0.5000000000 0.5000000000 0.5000000000

Format:

• Lines 1-3: Lattice vectors (3x3 matrix, one vector per line)

• Line 4: Number of atoms in the unit cell

• Line 5+: Fractional coordinates of each atom

Hopping File (zvo_hr.dat)

This file defines the hopping (transfer) integrals in Wannier90 format:

wannier90 format for vmcdry.out or HPhi -sdry
         1
         9
    1    1    1    1    1    1    1    1    1
   -1   -1    0    1    1    0.0  0.0
   -1    0    0    1    1   -1.0  0.0
   ...

Format:

• Line 1: Header comment

• Line 2: Number of Wannier functions

• Line 3: Number of R vectors

• Line 4: Degeneracy weights for each R vector

• Lines 5+: Hopping data (R_x, R_y, R_z, orbital_i, orbital_j, Re(t), Im(t))

Interaction File (zvo_ur.dat)

This file defines the on-site interaction in the same format as the hopping file:

wannier90 format for vmcdry.out or HPhi -sdry
         1
         9
    1    1    1    1    1    1    1    1    1
   -1   -1    0    1    1    0.0  0.0
   ...
    0    0    0    1    1    1.0  0.0
   ...

The entry at R = (0, 0, 0) with value 1.0 represents the on-site Hubbard U.

File Relationships

stan.in
  |
  +-- lattice = "wannier90"
        |
        +-- zvo_geom.dat  (geometry)
        +-- zvo_hr.dat    (hopping t)
        +-- zvo_ur.dat    (interaction U)

When lattice = "wannier90" is specified, StdFace automatically looks for these Wannier90 format files in the same directory as the input file.

Running the Example

cd samples/hubbard/wannier
../../../build/hphi_dry.out stan.in

Ensure all four files (stan.in, zvo_geom.dat, zvo_hr.dat, zvo_ur.dat) are present in the working directory.

When to Use Wannier90 Format

Use Wannier90-based input when:

• You have an existing tight-binding model from DFT+Wannier90 calculations

• You need custom hopping patterns not supported by built-in lattices

• You want to import realistic band structures from first-principles calculations

For simple models with standard lattice geometries, the default approach (built-in lattice constructors) is recommended.

Lattice Types Reference

StdFace supports the following built-in lattice types:

Lattice	Dimensions	Description
chain	1D	Linear chain
ladder	1D	Two-leg or multi-leg ladder
square	2D	Square lattice
triangular	2D	Triangular lattice
honeycomb	2D	Honeycomb (hexagonal) lattice
kagome	2D	Kagome lattice
tetragonal	3D	Tetragonal lattice
orthorhombic	3D	Orthorhombic/cubic lattice
fcortho	3D	Face-centered orthorhombic lattice
pyrochlore	3D	Pyrochlore lattice
wannier90	Any	Import from Wannier90 format files

See the developer documentation for implementation details of each lattice constructor.