Dualization of ingappabilities through Hilbert-space extensions

TL;DR

This paper introduces a Hilbert-space extension method to dualize quantum ingappabilities into discrete height models, revealing protection by a novel modulating translation symmetry and generalizing to higher-form gauge theories.

Contribution

It develops a rigorous dualization approach for quantum ingappabilities and uncovers a new symmetry protection mechanism, extending to higher-dimensional gauge theories.

Findings

Dualization of quantum ingappabilities achieved via Hilbert-space extensions.

Identification of a modulating translation symmetry protecting the ingappabilities.

Generalization of the framework to higher-form gauge fields in arbitrary dimensions.

Abstract

Typical dualities in arbitrary dimensions are understood through a Hilbert-space extension method. By these results, we rigorously dualize the quantum ingappabilities to discrete height model in one dimension which is inaccessible by earlier work such as flux-insertion arguments. It turns out that the ingappabilities of quantum discrete height model is protected by an exotic "modulating" translation symmetry, which is a combination of modulating internal symmetry transformation and the conventional lattice translation. It can be also generalize to higher-form gauge fields in arbitrary dimensions, e.g., $\mathbb{Z}$-gauge theory in two dimensions with $\mathbb{Z}$ one-form symmetry and a modulating translation symmetry.