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.

arXiv commentPublished version: 27 pages, 5 figures

References in corpus (46)

• Topological Insulators
• Topological insulators and superconductors
• Spintronics: Fundamentals and applications
• Many-Body Physics with Ultracold Gases
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Artificial gauge potentials for neutral atoms
• Anderson localization of a non-interacting Bose-Einstein condensate
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Light-induced gauge fields for ultracold atoms
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Experimental realization of a two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Quantum simulation of an extra dimension
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Synthetic 3D Spin-Orbit Coupling
• Quantum transport of disordered Weyl semimetals at the nodal point
• Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space
• 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
• Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices
• Quasi-relativistic behavior of cold atoms in light fields
• Hofstadter butterfly and integer quantum Hall effect in three dimensions
• Dirty Weyl semimetals: Stability, phase transition and quantum criticality
• 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
• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• (3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices
• Tilted disordered Weyl semimetals
• 2D spin-orbit coupling for ultracold atoms in optical lattices
• Duality and integer quantum Hall effect in isotropic 3D crystals
• Ultracold atoms in U(2) non-Abelian gauge potentials preserving the Landau levels
• Disordered double Weyl node: Comparison of transport and density-of-states calculations
• Disordered double Weyl node
• Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices
• PT invariant Weyl semimetals in gauge symmetric systems
• Quantum interference from sums over closed paths for electrons on a three-dimensional lattice in a magnetic field: total energy, magnetic moment, and orbital susceptibility
• Semimetal-superfluid quantum phase transitions in 2D and 3D lattices with Dirac points
• Omnidirectional spin Hall effect in a Weyl spin-orbit coupled atomic gas

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