Official Resources
- Homepage: https://github.com/xlhuang-phy/TopoTB
- Repository: https://github.com/xlhuang-phy/TopoTB
- License: GPL-3.0
Overview
TopoTB is a software package written in Mathematica for the interactive calculation and visualization of topological properties in tight-binding models. Its standout feature is its use of Mathematica's Manipulate functionality to create real-time interactive phase diagrams, allowing users to dynamically tune Hamiltonian parameters (like mass or hopping strength) and immediately see the effect on band structures, Berry curvature, and edge states.
Scientific domain: Topological Phases, Education, Model Building
Target user community: Theorists and Students exploring phase transitions
Theoretical Methods
- Tight-Binding: Symbolic or numerical Hamiltonian definitions.
- Topological Invariants:
- Chern Number: Integration of Berry curvature $\Omega_{xy}$.
- $\mathbb{Z}_2$ Invariant: Via Wilson loops or Parity criteria.
- Surface States: Slab calculations to reveal bulk-boundary correspondence.
Capabilities
- Interactive UI: Sliders to vary $t_1, t_2, \phi, M$, etc.
- Vizualization:
- 3D Band structures.
- Berry curvature density plots.
- Edge state dispersion.
- Invariants: Automatic calculation of Chern/Z2 numbers for the current parameter set.
- Phase Diagrams: Can scan parameters to map out phase boundaries (gap closings).
Key Strengths
- Interactivity: The ability to watch a gap close and the edge states change chirality in real-time is unmatched for pedagogical purposes and building intuition.
- Symbolic Power: Being based in Mathematica, it can handle analytic derivations of models before numerical evaluation.
- Ease of Entry: Requires no compilation, just dragging sliders.
Inputs & Outputs
- Inputs: Mathematica Notebook cells defining the lattice and Hamiltonian.
- Outputs: Interactive plots and numerical invariant values.
Interfaces & Ecosystem
- Platform: Requires Wolfram Mathematica.
- Language: Wolfram Language.
Performance Characteristics
- Speed: Fast for small "toy models" (2-8 bands) typical in topological physics. Slower for large supercells compared to compiled codes like C++ or Julia.
- Scalability: Not intended for large-scale atomistic simulations, but for model Hamiltonians.
Comparison with Other Codes
- vs. PythTB: PythTB is a Python library (script based). TopoTB is a Mathematica UI (interactive). TopoTB is better for "playing" with a model; PythTB is better for systematic scripting.
- vs. Kwant: Kwant is for transport. TopoTB is for band topology.
Application Areas
- Education: Demonstrating the Haldane model or Kane-Mele model in class.
- Research: Rapidly checking the topology of a new effective Hamiltonian.
Community and Support
- Development: Xielin Huang.
- Source: GitHub.
Verification & Sources
- Primary Publication: X. Huang et al., arXiv:2403.08615 (2024).
- Verification status: ✅ VERIFIED