A higher-order topological twist on cold-atom SO(5) Dirac fields

TL;DR

This paper proposes using ultracold spin-3/2 Fermi gases in a 2D Raman lattice as a quantum simulator for higher-order topological states in Dirac quantum field theories with SO(5) symmetry, revealing a rich phase diagram.

Contribution

It introduces a novel approach to realize higher-order topological states with tunable interactions using cold-atom systems simulating SO(5) Dirac fields with 4-Fermi interactions.

Findings

Identification of a lattice regularization with twisted Wilson mass

Discovery of a phase diagram with competing fermion condensates

Access to higher-order topological states protected by SO(5) symmetry

Abstract

Ultracold Fermi gases of spin-3/2 atoms provide a clean platform to realise SO(5) models of 4-Fermi interactions in the laboratory. By confining the atoms in a two-dimensional Raman lattice, we show how this system can be used as a flexible quantum simulator of Dirac quantum field theories (QFTs) that combine Gross-Neveu and Thirring interactions with a higher-order topological twist. We show that the lattice model corresponds to a regularization of this QFT with an anisotropic twisted Wilson mass. This allows us to access higher-order topological states protected by a hidden SO(5) symmetry, a remnant of the original rotational symmetry of the 4-Fermi interactions that is not explicitly broken by the lattice discretization. Using large-$N$ methods, we show that the 4-Fermi interactions lead to a rich phase diagram with various competing fermion condensates. Our work opens a route for the implementation of correlated higher-order topological states with tunable interactions that has interesting connections to non-trivial relativistic QFTs of Dirac fermions in $D = 2 + 1$ dimensions.