TBmodels

Official Resources

• Homepage: https://tbmodels.greschd.ch/
• Documentation: https://tbmodels.greschd.ch/en/latest/
• Repository: https://github.com/Z2PackDev/TBmodels
• License: GPL-3.0

Overview

TBmodels is a Python library developed as part of the Z2Pack ecosystem, designed for reading, creating, and manipulating tight-binding models. Its distinct feature is its comprehensive support for symmetry operations and seamless integration with Wannier90. It allows users to read Wannier Hamiltonians, symmetrize them to enforce crystal symmetries, and export them for topological invariant calculations, making it a critical tool in the workflow for identifying topological materials.

Scientific domain: Topological Materials, Symmetry Analysis Target user community: Researchers using Wannier90 for topological characterization

Theoretical Methods

• Tight-Binding: Evaluation of $H(\mathbf{k}) = \sum_{\mathbf{R}} e^{i\mathbf{k}\cdot\mathbf{R}} H(\mathbf{R})$.
• Symmetry Analysis:
  • Application of space group operations to effective models.
  • Symmetrization: $\tilde{H} = \frac{1}{|G|} \sum_{g \in G} D(g) H(g^{-1} \mathbf{k}) D^\dagger(g)$.
• Interpolation: Fourier transform from real-space Wannier representation to k-space.

Capabilities

• Model Construction:
  • Direct import from wannier90_hr.dat.
  • Manual construction from hopping terms.
  • HDF5 storage for efficient I/O.
• Manipulation:
  • Supercell creation.
  • Dimensionality reduction (slab cutting).
  • Basis transformation.
• Observables:
  • Band structures.
  • Eigenvalues/Eigenvectors along paths.
• Symmetry: Extensive tools to check and enforce symmetries on numerical models.

Key Strengths

• Wannier90 Integration: The from_wannier_files() method is robust and handles the wsvec.dat (Wigner-Seitz vectors) correctly, solving phase ambiguity issues common in other parsers.
• Topology Ready: Directly feeds into Z2Pack for calculating Wilson loops and Chern numbers.
• Sparse Storage: Efficiently handles large models with many hopping terms using sparse matrix logic.

Inputs & Outputs

• Inputs:
  • Wannier90 output files (_hr.dat, _wsvec.dat).
  • Python scripts.
• Outputs:
  • HDF5 model files.
  • Band structure arrays.

Interfaces & Ecosystem

• Z2Pack: Primary consumer of TBmodels objects.
• Wannier90: Primary source of input data.
• PythTB: TBmodels can convert to/from PythTB formats.

Performance Characteristics

• Efficiency: Optimized for evaluating Hamiltonians at many k-points (vectorized via NumPy).
• Scalability: Handles models with hundreds of orbitals (standard Wannier output).

Comparison with Other Codes

• vs. PythTB: PythTB is excellent for pedagogy and simple models. TBmodels is built for the "read Wannier90 $\to$ symmetrize $\to$ calculate Z2" research pipeline.
• vs. Pybinding: Pybinding is better for massive disordered systems (KPM). TBmodels is better for accurate bulk topology of crystals.

Application Areas

• Material Discovery: Screening databases for topological insulators.
• Surface States: Constructing slab models from bulk Wannier functions to see surface bands.

Community and Support

• Development: Dominik Gresch (ETH Zurich alumni).
• Source: GitHub.

Verification & Sources

• Website: https://tbmodels.greschd.ch/
• Verification status: ✅ VERIFIED
  • Mature library in the topological physics stack.