Fractal symmetries: Ungauging the cubic code

TL;DR

This paper develops a gauging procedure for submanifold symmetries, including fractal types, and demonstrates how it relates to topological phases and the cubic code, expanding understanding of entangled quantum phases.

Contribution

It introduces a general gauging method for fractal and submanifold symmetries in Pauli Hamiltonians, linking models and constructing new entangled phases.

Findings

Gauging relates models with fractal symmetries to topological phases.

Constructs short-range entangled phases with fractal-like symmetries.

Maps certain phases to the cubic code via gauging.

Abstract

Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure for general submanifold symmetries of Pauli Hamiltonians, including symmetries of fractal type. We show a relation between the pre- and post-gauging models and use this to construct short-range entangled phases with fractal-like symmetries, one of which is mapped to the cubic code by the gauging.