Correlated Topological Phases and Exotic Magnetism with Ultracold Fermions

TL;DR

This paper explores how ultracold fermions in optical lattices can realize complex topological phases and exotic magnetic orders through engineered gauge fields, spin-orbit coupling, and strong interactions, revealing rich phase diagrams.

Contribution

It introduces a non-Abelian Hofstadter-Hubbard model with spin-orbit coupling, analyzing its topological and magnetic phases using advanced theoretical and numerical methods.

Findings

Identification of interaction-induced topological phase transitions

Mapping of magnetic phase diagram with exotic magnetic orders

Demonstration of rich topological and magnetic phenomena in ultracold fermion systems

Abstract

Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter-Hubbard model. We include an additional staggered lattice potential and an artificial Rashba--type spin-orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interaction-induced transition from normal to topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba--type spin-orbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.