Gauge fields emerging from time reversal symmetry breaking for spin-5/2 fermions in a honeycomb lattice

TL;DR

This paper explores how spin-5/2 fermions in a honeycomb lattice can spontaneously break time reversal symmetry, leading to emergent gauge fields, chiral spin liquids, and quantum Hall effects, with implications for simulating lattice gauge theories.

Contribution

It introduces a feasible ultracold atom setup to simulate gauge theories with emergent gauge fields from time reversal symmetry breaking in spin-5/2 fermions.

Findings

Ground state is a chiral spin liquid with flux per plaquette.

System exhibits quantum Hall effect and chiral edge states.

Spin fluctuations relate to gauge field dynamics.

Abstract

We propose an experimentally feasible setup with ultracold alkaline earth atoms to simulate the dynamics of U(1) lattice gauge theories in 2+1 dimensions with a Chern-Simons term. To this end we consider the ground state properties of spin-5/2 alkaline earth fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin liquid state with $2\pi/3$ flux per plaquette, which spontaneously violates time reversal invariance. We demonstrate that due to the breaking of time reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge field dynamics. We discuss also properties of the lowest energy competing orders.