Topology-ferrimagnetism intertwining via weak interactions in Lieb lattices

TL;DR

This paper demonstrates the emergence of magnetic topological states with spontaneous symmetry breaking in a Lieb lattice, combining experimental feasibility with theoretical insights into weak interaction regimes.

Contribution

It introduces an experimentally accessible platform for magnetic topological states in a spin-orbit-coupled Lieb lattice, revealing coexistence of topological order and ferrimagnetism.

Findings

Coexistence of topological characteristics and ferrimagnetism in ground states

Magnetic topological insulators emerge under weak interactions

Proposed ultracold atom implementation scheme

Abstract

A common wisdom about quantum many-body systems is that emergent phases typically fall into either the Landau-Ginzburg paradigm or topological classifications. Experimentally realizing the intertwined emergence of spontaneous symmetry breaking and topological order remains challenging. Here, we present an experimentally accessible platform for studying magnetic topological states in a spin-orbit-coupled Lieb lattice. Remarkably, we observe the coexistence of topological characteristics, quantified by the Chern number and Bott index, with spontaneous symmetry-breaking orders, such as ferrimagnetism, in the many-body ground states. Computational analyses combining dynamical mean-field theory and Hartree-Fock approximations reveal a pronounced parameter regime where magnetic topological insulators emerge even under weak interactions. This unconventional phenomenon originates from the Lieb lattice's unique band structure, which facilitates the synergy between interaction-driven symmetry breaking and spin-orbit coupling induced band inversion. Crucially, spin polarization and spin winding co-emerge as inherently coupled phenomena due to their shared origin in the same interacting, spinful atoms. We further propose a specific experimental implementation scheme for ultracold atoms, utilizing currently available Raman lattice techniques. Our findings pave the way for exploring the interplay between symmetry-broken states and topological order in strongly correlated systems.