Correlated Chern insulators in two-dimensional Raman lattices: A cold-atom regularization of strongly coupled four-Fermi field theories

Abstract

We show that synthetic spin-orbit coupling for ultracold atoms in optical Raman potentials can be exploited to build versatile quantum simulators of correlated Chern insulators connected to strongly coupled four-Fermi field theories similar to the Gross-Neveu model in (2+1) dimensions. Exploiting this multidisciplinary perspective, we identify a large-N quantum anomalous Hall (QAH) effect in absence of any external magnetic field, and use it to delimit regions in parameter space where these correlated topological phases appear, the boundaries of which are controlled by strongly coupled fixed points of these four-Fermi relativistic field theories. We further show how, for strong interactions, the QAH effect gives way to magnetic phases described by a two-dimensional quantum compass model in a transverse field. We present a detailed description of the phase diagram using the large-N effective potential, and variational techniques such as projected entangled pairs.Received 22 December 2020Revised 8 July 2022Accepted 25 July 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L042012Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChern insulatorsLattice field theoryOptical lattices & trapsQuantum simulationAtomic, Molecular & OpticalQuantum InformationCondensed Matter, Materials & Applied Physics