Correlated Topological Phases and Exotic Magnetism with Ultracold Fermions

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.

17 pages, 7 figures. Contribution to J. Phys. B special issue on non-Abelian gauge fields

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• Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Topological Mirror Insulators in One Dimension
• Quantum magnetism of bosons with synthetic gauge fields in one-dimensional optical lattices: a Density Matrix Renormalization Group study
• Chiral Bosonic Phases on the Haldane Honeycomb Lattice
• Interaction-Induced Topological and Magnetic Phases in the Hofstadter-Hubbard Model
• Interacting Hofstadter Interface
• Dimensional crossover and cold-atom realization of topological Mott insulators
• Artificial $SU(3)$ Spin-Orbit Coupling and Exotic Mott Insulators
• Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
• Anisotropic Quantum Spin Hall Effect, Spin-Orbital Textures and Mott Transition
• Orbital Effect of the Magnetic Field in Dynamical Mean-Field Theory
• Lattice symmetry and emergence of antiferromagnetic quantum Hall states
• Local Chern marker of smoothly confined Hofstadter fermions
• Quantum phases of strongly-interacting bosons on a two-leg Haldane ladder
• Topological Mott transition in a Weyl-Hubbard model with dynamical mean-field theory
• Realizing Topological Mott Insulators from the RKKY Interaction
• Spin-imbalance-induced transverse magnetization in the Hofstadter-Hubbard model
• Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling
• Fractional topological insulator precursors in spin-orbit fermion ladders