HofstadterTools: A Python package for analyzing the Hofstadter model

Abstract

The Hofstadter model successfully describes the behavior of non-interacting quantum particles hopping on a lattice coupled to a gauge field, and hence is ubiquitous in many fields of research, including condensed matter, optical, and atomic physics. Motivated by this, we introduce HofstadterTools (https://hofstadter.tools), a Python package that can be used to analyze the energy spectrum of a generalized Hofstadter model, with any combination of hoppings on any regular Euclidean lattice. The package can be applied to compute key properties of the band structure, such as quantum geometry and topology, as well as plot Hofstadter butterflies and Wannier diagrams that are colored according to their Chern numbers.

7 pages, 4 figures

References in corpus (3)

• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Spectral signatures of many-body localization with interacting photons
• The Colored Hofstadter Butterfly for the Honeycomb Lattice

Cited by in corpus (3)

• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Universal Performance Gap of Neural Quantum States Applied to the Hofstadter-Bose-Hubbard Model
• Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model