Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment

TL;DR

This paper explores how topological and symmetry considerations influence quantum phase transitions in 2+1D Dirac fermion models, revealing complex phase diagrams and the impact of topological terms on transition order.

Contribution

It introduces models with specific symmetries that exhibit diverse phases and transitions, including a deconfined quantum critical point and the effects of topological terms on transition nature.

Findings

Rich phase diagram for N=2 with multiple phases

Observation of a deconfined quantum critical point at N=1

Numerical results show a strong first order transition at N=2

Abstract

Topology plays a cardinal role in explaining phases and quantum phase transitions beyond the Landau-Ginzburg-Wilson paradigm. In this study, we formulate a set of models of Dirac fermions in 2+1 dimensions with SU($N$)$\times$SU(2)$\times$U(1) symmetry that have the potential to host critical points described by field theories with topological terms. For $N=2$ it shows a rich phase diagram containing semimetallic, quantum spin Hall insulating, Kekul\'e valence bond solid and s-wave superconducting phases and features multiple Landau-Ginzburg-Wilson phase transitions driven by interaction strength. At $N=1$ a deconfined quantum critical point is observed. At $N=2$ one expects the critical theory to correspond to a level 2 Wess-Zumino-Witten theory in 2+1 dimensions. Here the numerical results however show a strong first order transition. Another transition can be governed by a topological $\theta$-term which is rendered irrelevant for even values of $N$ thus leading to Landau-Ginzburg-Wilson behaviour.