Duality viewpoint of criticality

TL;DR

This paper explores the criticality of self-dual quantum many-body systems with symmetry protected topological phases, revealing ground state degeneracy and anomalies at critical points, applicable to various symmetries.

Contribution

It provides a geometric framework to understand criticality in self-dual models and predicts their spectra considering different symmetry types, including higher form and subsystem symmetries.

Findings

Ground state degeneracy under periodic boundary conditions.

Symmetry group at criticality exhibits mixed 't Hooft anomaly.

Applicable to models with ordinary and generalized symmetries.

Abstract

In this work, we study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological (SPT) phases. We provide a geometric explanation of the criticality of these self-dual models. More precisely, we show a ground state (quasi-)degeneracy under the periodic boundary conditions,i.e., the ingappability of the bulk spectrum. Equivalently, the symmetry group at criticality, including the duality symmetry, has a mixed 't Hooft anomaly. This approach can not only predict the spectrum of the self-dual model with ordinary 0-form symmetry, but also be applied to that with generalized symmetry, such as higher form and subsystem symmetry. As an application, we illustrate our results with several examples in one and two dimensions, which separate two different SPTs.