Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials

Abstract

We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general space-independent non-Abelian gauge potential. We first review and analyze the case of purely Abelian potentials, showing also that the so-called Hasegawa gauge yields a decomposition of the Hamiltonian into sub-matrices having minimal dimension. Explicit expressions for such matrices are derived, also for general anisotropic fluxes. Later on, we show that the introduction of a translational invariant non-Abelian coupling for multi-component spinors does not affect the dimension of the minimal Hamiltonian blocks, nor the dimension of the magnetic Brillouin zone. General formulas are presented for the U(2) case and explicit examples are investigated involving $\pi$ and $2\pi /3$ magnetic fluxes. Finally, we numerically study the effect of random flux perturbations.

Published version: 27 pages, 5 figures

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Classification of topological insulators and superconductors in three spatial dimensions
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• BCS-BEC crossover induced by a synthetic non-Abelian gauge field
• Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice
• Quasi-relativistic behavior of cold atoms in light fields
• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
• Massless Dirac Fermions in a Square Optical Lattice
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
• Tilted disordered Weyl semimetals

Cited by in corpus (2)

• Topological van Hove singularities at phase transitions in Weyl metals
• Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model