Competing Orders and Anomalies

TL;DR

This paper explores how quantum anomalies influence phase transitions between competing orders, revealing that anomalies enforce massless excitations and define distinct universality classes, with implications for understanding quantum many-body systems.

Contribution

It explicitly calculates topological anomalies in non-linear sigma models with WZW terms and establishes non-perturbative criteria for quantum phase transitions based on anomaly matching.

Findings

Anomalies enforce massless excitations across phase diagrams.

Different theories with competing orders can belong to distinct universality classes.

Physical realizations and experimental implications of anomalies are discussed.

Abstract

A conservation law is one of the most fundamental properties in nature, but a certain class of conservation "laws"' could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies have deepened our understanding in quantum many body systems. Here, we investigate quantum anomaly effects in quantum phase transitions between competing orders and striking consequences of their presence. We explicitly calculate topological nature of anomalies of non-linear sigma models (NLSMs) with the Wess-Zumino-Witten (WZW) terms. The non-perturbative nature is directly related with the 't Hooft anomaly matching condition : anomalies are conserved in renormalization group flow. By applying the matching condition, we show massless excitations are enforced by the anomalies in a whole phase diagram in sharp contrast to the case of the Landau-Ginzburg-Wilson theory which only has massive excitations in symmetric phases. Furthermore, we find non-perturbative criteria to characterize quantum phase transitions between competing orders. For example, in 4D, we show the two competing order parameter theories, CP(1) and the NLSM with WZW, describe different universality class. Physical realizations and experimental implication of the anomalies are also discussed.