Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup

TL;DR

This paper explores how gauging a finite subgroup in a system with global symmetry can lead to novel gapless topological phases and deconfined critical points, demonstrated through a $ ext{U}(1)$-symmetric Bose-Hubbard model in 1D and 2D.

Contribution

It introduces the concept of partial gauging to construct and analyze new gapless SPT phases and generalized deconfined quantum critical points in bosonic systems.

Findings

Superfluid phase maps to a gapless SPT phase in 1D.

The superfluid-insulator transition in 2D becomes a generalized deconfined quantum critical point.

Identification of an emergent mixed 't Hooft anomaly between symmetries.

Abstract

Gauging a finite subgroup of a global symmetry can map conventional phases and phase transitions to unconventional ones. In this work, we study, as a concrete example, an emergent $\mathbb{Z}_2$-gauged system with global symmetry $U(1)$, namely, the $\mathbb{Z}_2$-gauged Bose-Hubbard model both in 1-D and in 2-D. In certain limits, there is an emergent mixed 't Hooft anomaly between the quotient $\tilde{U}(1)$ symmetry and the dual $\hat{\mathbb{Z}}_2$ symmetry. In 1-D, the superfluid phase is mapped to an intrinsically gapless symmetry-protected topological (SPT) phase, as supported by density-matrix renormalization group (DMRG) calculations. In 2-D, the original superfluid-insulator transition becomes a generalized deconfined quantum critical point (DQCP) between a gapless SPT phase, where a SPT order coexists with Goldstone modes, and a $\tilde{U}(1)$-symmetry-enriched topological (SET) phase. We also discuss the stability of these phases and the critical points to small perturbations and their potential experimental realizations. Our work demonstrates that partial gauging is a simple and yet powerful approach in constructing novel phases and quantum criticalities.