Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices

TL;DR

This study uses large-scale Monte Carlo simulations to investigate whether emergent continuous symmetries occur at quantum critical points in frustrated Ising models on triangle and honeycomb lattices, revealing different behaviors in each case.

Contribution

It provides the first comprehensive numerical comparison showing emergent O(2) symmetry in the triangle lattice TFFIM and a first-order transition without such symmetry in the honeycomb lattice TFFIM.

Findings

Emergent O(2) symmetry in triangle lattice TFFIM

First-order quantum phase transition in honeycomb lattice TFFIM

Anisotropic terms determine the presence or absence of continuous symmetry

Abstract

Continuous symmetries are believed to emerge at many quantum critical points in frustrated magnets. In this work, we study two candidates of this paradigm: the transverse-field frustrated Ising model (TFFIM) on the triangle and the honeycomb lattices. The former is the prototypical example of this paradigm, and the latter has recently been proposed as another realization. Our large-scale Monte Carlo simulation confirms that the quantum phase transition (QPT) in the triangle lattice TFFIM indeed hosts an emergent O(2) symmetry, but that in the honeycomb lattice TFFIM is a first-order QPT and does not have an emergent continuous symmetry. Furthermore, our analysis of the order parameter histogram reveals that such different behavior originates from the irrelevance and relevance of anisotropic terms near the QPT in the low-energy effective theory of the two models. The comparison between theoretical analysis and numerical simulation in this work paves the way for scrutinizing investigation of emergent continuous symmetry at classical and quantum phase transitions.