Multipole and fracton topological order via gauging foliated SPT phases

TL;DR

This paper introduces a method to construct topological phases with multipole symmetries and fracton order by gauging layered SPT phases, providing insights into their field theories and excitations.

Contribution

It presents a novel construction of multipole and fracton topological phases through gauging layered SPT phases, enhancing understanding of their field theories and excitations.

Findings

Constructed topological phases with multipole symmetries via gauging layered SPTs

Altered fractional excitation statistics across SPT phases

Provided a framework for understanding field theories of fracton models

Abstract

Spurred by recent development of fracton topological phases, unusual topological phases possessing fractionalized quasi-particles with mobility constraints, the concept of symmetries has been renewed. In particular, in accordance with the progress of multipole symmetries, associated with conservation of multipoles, such as dipole or quadruple moments as well as global charges, there have been proposed topological phases with such symmetries. These topological phases are unconventional as excitations are subject to mobility constraints corresponding to the multipole symmetries. We demonstrate a way to construct such phases by preparing layers of symmetry protected topological (SPT) phases and implementing gauging a global symmetry. After gauging, the statistics of a fractional excitation is altered when crossing the SPT phases, resulting in topological phases with the multipole symmetries. The way we construct the phases allows us to have a comprehensive understanding of field theories of topological phases with the multipole symmetries and other fracton models.