Charged fermions coupled to $\mathbb{Z}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions

TL;DR

This paper studies a 2+1D model of charged fermions coupled to a $ ext{Z}_2$ gauge field, revealing a rich phase diagram with superfluidity, confinement, and emergent Dirac fermions, using sign problem free quantum Monte Carlo methods.

Contribution

It introduces a novel method to handle the Gauss law constraint in sign problem free determinantal quantum Monte Carlo for this model, and uncovers new insights into the phase transitions and emergent phenomena.

Findings

Superfluidity appears in both deconfined and confined phases.

A continuous transition exists between the deconfined Dirac phase and the confined superfluid.

Emergent Dirac fermions are stable against pairing at certain flux phases.

Abstract

We consider a 2+1 dimensional model of charged fermions coupled to a $\mathbb{Z}_2$ gauge field, and study the confinement transition in this regime. To elucidate the phase diagram of this model, we introduce a method to handle the Gauss law constraint within sign problem free determinantal quantum Monte Carlo, at any charge density. For generic charge densities, $\mathbb{Z}_2$ gauge fluctuations mediate pairing and the ground state is a gapped superfluid. Superfluidity also appears in the confined phase. This is reminiscent of the BCS-BEC crossover, except that a true zero temperature transition occurs here, with the maximum $T_c$ achieved near the transition. At half-filling also one obtains a large Fermi surface which is gapped at zero temperature. However, on increasing fermion hopping a $\pi$-flux phase is spontaneously generated, with emergent Dirac fermions that are stable against pairing. In contrast to a Fermi liquid of electrons, the change in Fermi surface volumes of the $\mathbb{Z}_2$ fermions occurs without the breaking of translation symmetry. Unexpectedly, the numerics indicate a single continuous transition between the deconfined Dirac phase and the confined superfluid, in contrast to the naive expectation of a split transition, where a gap to fermions precedes confinement.