Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

Abstract

We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving non-trivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal/insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system and the topological phase transitions can be detected by analyzing its polarization in time of flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.

arXiv commentPublished version with several extensions and improvements, 13 pages, 10 figures

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• Quantum simulation of non-trivial topology
• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• Current transport properties and phase diagram of a Kitaev chain with long-range pairing
• Simulation of non-Abelian lattice gauge fields with a single component gas
• Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder
• Strange correlators for topological quantum systems from bulk-boundary correspondence
• Flat bands and $Z_2$ topological phases in a non-Abelian kagome lattice
• Spin-orbit-coupled atomic Fermi gases in two-dimensional optical lattices in the presence of a Zeeman field
• Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
• Phase diagram, band structure and density of states in two-dimensional attractive Fermi-Hubbard model with Rashba spin-orbit coupling
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels