Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations

TL;DR

This paper introduces a non-invertible duality transformation to systematically construct and analyze intrinsically gapless symmetry protected topological phases, expanding understanding beyond decorated defect models.

Contribution

It develops a method using non-invertible duality transformations to construct and study new types of gapless SPT phases, including purely gapless ones without gapped sectors.

Findings

Reproduces known gapless SPT examples via decorated defect constructions.

Constructs new purely gapless SPT phases beyond decorated defect models.

Provides a field theory framework for analyzing stability of gapless SPTs.

Abstract

The Kennedy-Tasaki (KT) transformation was used to construct the gapped symmetry protected topological (SPT) phase from the symmetry breaking phase with open boundary condition, and was generalized in our proceeding work [L. Li et al. arXiv:2301.07899] on a ring by sacrificing the unitarity, and should be understood as a non-invertible duality transformation. In this work, we further apply the KT transformation to systematically construct gapless symmetry protected topological phases. This construction reproduces the known examples of (intrinsically) gapless SPT where the non-trivial topological features come from the gapped sectors by means of decorated defect constructions. We also construct new (intrinsically) purely gapless SPTs where there are no gapped sectors, hence are beyond the decorated defect construction. This construction elucidates the field theory description of the various gapless SPTs, and can also be applied to analytically study the stability of various gapless SPT models on the lattice under certain symmetric perturbations.