Symmetric approximant formalism for statistical topological matter

This repository contains the code and data for "Symmetric approximant formalism for statistical topological matter" by R. Johanna Zijderveld, Adam Yanis Chaou, Isidora Araya Day, and Anton R. Akhmerov. Installation This project uses [pixi](https://pixi.sh) for dependency management: ```bash pixi install ``` Generating Figures and Manuscript Generate all figures from the data: ```bash pixi run generate_results ``` This will: 1. Execute all scripts in `results/` to generate figures 2. Convert SVG figures to PDF Regenerating Simulation Data The raw data in `data/` can be regenerated using the scripts in `simulations/`. These scripts are designed to run on an HPC cluster, but individual point calculation is also included. - `invariant_conductance_mirror.py` - Computes the mirror invariant and both symmetrized and unsymmetrized conductance. - `invariant_conductance_glide.py` - Computes the glide invariant and conductance. - `invariant_conductance_I.py` - Computes determinant invariants for Corbino disk geometry with inversion symmetry Each script uses the `adaptive` library for efficient parameter space sampling and saves results to `data/`. Numerical Validation The `simulations/check_condition_number.py` script validates that the scattering matrices computed by Kwant are numerically well-behaved. It extracts MUMPS solver diagnostics including: - Condition number estimates - Relative error bounds - Omega parameters for iterative refinement This ensures the S-matrix calculations remain accurate even for large system sizes and near phase transitions where numerical instabilities could arise. Acknowledgements This project reuses code from the "Scattering theory of higher order topological phases", by R. Johanna Zijderveld, Isidora Araya Day, and Anton R. Akhmerov, https://zenodo.org/records/15553181, DOI: 10.5281/zenodo.14503341. During the development of this code we have used AI-based tools ChatGPT and Github copilot chat to perform the following: generate code and text typing suggestions and generate and modify code based on a sequence of prompts. We have reviewed the AI-generated code.