Noninvertible Symmetry-Enriched Quantum Critical Point

TL;DR

This paper explores a new class of quantum critical points enriched by noninvertible symmetries, revealing their unique properties and phase transition behaviors in one-dimensional lattice models.

Contribution

It introduces noninvertible symmetry-enriched quantum critical points as a generalization of known symmetry-enriched critical points, using the Rep(D8) symmetry in 1D lattice models.

Findings

Identified low-energy properties of noninvertible symmetry-enriched QCPs.

Demonstrated phase transitions between different SPT and SSB phases involving noninvertible symmetries.

Showed that these QCPs cannot be connected without a phase transition or multi-critical point.

Abstract

Noninvertible symmetry generalizes traditional group symmetries, advancing our understanding of quantum matter, especially one-dimensional gapped quantum systems. In critical lattice models, it is usually realized as emergent symmetries in the corresponding low-energy conformal field theories. In this work, we study critical lattice models with the noninvertible Rep($D_8$) symmetry in one dimension. This leads us to a new class of quantum critical points (QCP), noninvertible symmetry-enriched QCPs, as a generalization of known group symmetry-enriched QCPs. They are realized as phase transitions between one noninvertible symmetry-protected topological (SPT) phase and another different one or spontaneous symmetry breaking (SSB) phase. We identify their low-energy properties and topological features through the Kennedy-Tasaki (KT) duality transformation. We argue that distinct noninvertible symmetry-enriched QCPs can not be smoothly connected without a phase transition or a multi-critical point.