Quasisymmetry Enriched Gapless Criticality at Chern Insulator Transitions

TL;DR

This paper introduces quasisymmetry as a key concept in continuous topological phase transitions, revealing new regulated phenomena and enriching the classification of quantum criticality in Chern insulator transitions.

Contribution

It identifies quasisymmetries in gapless subspaces of topological transitions, providing a new framework for understanding critical phenomena and generalized Hall responses.

Findings

Quasisymmetries subdivide transitions by charge

Regulated charge-current correlations observed

Generalized Hall conductivities follow a modified Streda formula

Abstract

In continuous topological phase transitions (CTPTs), the low-energy physics is governed by gap-closing subspaces, where approximate "higher" symmetries, termed quasisymmetries, may emerge. Here, we introduce the notion of quasisymmetry enrichment of these transitions. Focusing on paradigmatic normal-to-Chern insulator transitions, we identify quasisymmetries in the gapless subspaces, which subdivide CTPTs of the same universality class according to quasisymmetry charges. Gapless criticalities with nontrivial charges exhibit regulated phenomena, including intrinsic correlations between charge and pseudospin currents and continuous generalized Hall conductivities governed by the generalized St\v{r}eda formula, both conventionally exclusive to gapped phases. These features arise as quasisymmetry forbids certain matrix elements, rendering the generalized Berry curvature integrable. By establishing quasisymmetry as a fundamental classifying ingredient, our work adds a new dimension for understanding the rich landscape of quantum phase transitions.