Simulation of Fermionic and Bosonic Critical Points with Emergent SO(5) Symmetry

TL;DR

This paper uses quantum Monte Carlo simulations to demonstrate emergent SO(5) symmetry at critical points in a 2+1D Dirac fermion model with competing phases, revealing new insights into quantum phase transitions.

Contribution

It provides numerical evidence for emergent SO(5) symmetry at multicritical and deconfined critical points in a fermionic lattice model, connecting algebraic properties to critical phenomena.

Findings

Operator rotating between QSHI and SSC commutes at criticality

Emergent SO(5) symmetry observed at critical points

Gap in the operator within ordered phases

Abstract

We introduce a model of Dirac fermions in 2+1 dimensions with a semimetallic, a quantum spin-Hall insulating (QSHI), and an s-wave superconducting (SSC) phase. The phase diagram features a multicritical point at which all three phases meet as well as a QSHI-SSC deconfined critical point. The QSHI and SSC orders correspond to mutually anti-commuting mass terms of the Dirac Hamiltonian. Based on this algebraic property, SO(5) symmetric field theories have been put forward to describe both types of critical points. Using quantum Monte Carlo simulations, we directly study the operator that rotates between QSHI and SSC states. The results suggest that it commutes with the low-energy effective Hamiltonian at criticality but has a gap in the ordered phases. This implies an emergent SO(5) symmetry at both the multicritical and the deconfined critical points.