Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry

TL;DR

This paper studies a 2+1D Dirac fermion model with competing orders, revealing a continuous transition with emergent SO(4) symmetry and deconfined quantum criticality, supported by sign-free quantum Monte Carlo simulations.

Contribution

It introduces a sign-free model of Dirac fermions with competing orders, demonstrating a non-Landau continuous transition with emergent symmetry and a new framework for exotic critical phenomena.

Findings

Identifies a continuous Neel-Kekule9 transition with emergent SO(4) symmetry.

Supports deconfined quantum criticality interpretation of the transition.

Features a tricritical point where multiple phases meet.

Abstract

We consider a model of Dirac fermions in $2+1$ dimensions with dynamically generated, anticommuting SO(3) N\'eel and Z$_2$ Kekul\'e mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the N\'eel and Kekul\'e phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While the bare symmetries of our model do not allow for spinon-carrying Z$_3$ vortices in the Kekul\'e mass, the emergent SO(4) invariance permits an interpretation of the transition in terms of deconfined quantum criticality. The phase diagram also features a tricritical point at which N\'eel, Kekul\'e, and semimetallic phases meet. The present, sign-free approach can be generalized to a variety of other mass terms and thereby provides a new framework to study exotic critical phenomena.