Interaction-Induced Topological and Magnetic Phases in the Hofstadter-Hubbard Model

Abstract

Interaction effects have been a subject of contemporary interest in topological phases of matter. But in the presence of interactions, the accurate determination of topological invariants in their general form is difficult due to their dependence on multiple integrals containing Green's functions and their derivatives. Here we employ the recently proposed "effective topological Hamiltonian" approach to explore interaction-induced topological phases in the time-reversal-invariant Hofstadter-Hubbard model. Within this approach, the zero-frequency part of the self-energy is sufficient to determine the correct topological invariant. We combine the topological Hamiltonian approach with the local self-energy approximation, both for the static and the full dynamical self-energy evaluated using dynamical mean field theory (DMFT), and present the resulting phase diagram in the presence of many-body interactions. We investigate the emergence of quantum spin Hall (QSH) states for different interaction strengths by calculating the ${\mathbb{Z}}_2$ invariant. The interplay of strong correlations and a staggered potential also induces magnetic long-range order with an associated first order transition. We present results for the staggered magnetization ( $m_s$ ), staggered occupancy ( $n_s$ ), and double occupancy across the transition.

9 pages, 9 figures

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• Dropping an impurity into a Chern insulator: a polaron view on topological matter
• Topological bound states in interacting Su-Schrieffer-Heeger rings
• Interactions enable Thouless pumping in a nonsliding lattice
• Interacting Hofstadter Interface
• Statistical Analysis of the Chern Number in the Interacting Haldane-Hubbard Model
• Tracing the nonequilibrium topological state of Chern insulators
• Fate of a topological invariant for correlated lattice electrons at finite temperature
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Temperature and doping induced instabilities of the repulsive Hubbard model on Lieb lattice
• Coexistence of metallic edge states and anti-ferromagnetic ordering in correlated topological insulators
• The Mott transition as a topological phase transition
• Interaction-enhanced integer quantum Hall effect in disordered systems
• Magnetization, d-wave superconductivity and non-Fermi liquid behavior in a crossover from dispersive to flat bands
• Orbital Effect of the Magnetic Field in Dynamical Mean-Field Theory
• Measuring the topological phase transition via the single-particle density matrix
• Local Chern marker of smoothly confined Hofstadter fermions
• Spin-orbit coupling in the kagome lattice with flux and time-reversal symmetry
• Topological Mott transition in a Weyl-Hubbard model with dynamical mean-field theory
• Self-Energy Dispersion in the Hubbard Model
• Spin-imbalance-induced transverse magnetization in the Hofstadter-Hubbard model
• Impact of magnetic dopants on magnetic and topological phases in magnetic topological insulators
• Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling
• Mott transition and magnetism in a fragile topological insulator
• Paramagnetic phases of strongly correlated ultracold fermions coupled to an optical cavity