Constructing Bulk Topological Orders via Layered Gauging

TL;DR

This paper introduces a layered gauging method to systematically construct various bulk topological orders from lower-dimensional symmetries, including fracton and topological orders, using a physically intuitive stacking and gauging procedure.

Contribution

The authors propose a versatile layered gauging construction that generalizes bulk topological order creation from diverse symmetry types, demonstrated through multiple examples.

Findings

Derived the X-cube fracton model from 2D subsystem symmetry.

Constructed a new model realizing double semion topological order from 1D anomalous symmetry.

Showed the method's applicability to conventional, higher-form, subsystem, anomalous, nonabelian, and noninvertible symmetries.

Abstract

Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates symmetries in $k$ dimensions to "bulk" topological orders in $(k+1)$ dimensions. While conceptually profound, most existing bulk construction methods rely on sophisticated mathematical formalisms and can be difficult to apply to certain symmetry types. In this work, we propose a physically intuitive and versatile method, termed the layered gauging construction, to systematically generate $(k+1)$-dimensional (liquid or fracton) topological orders from $k$-dimensional generalized symmetries. Roughly speaking, the prescription is to stack many layers of $k$-dimensional quantum systems with certain symmetries into a $(k+1)$-dimensional pile, and then sequentially gauge a diagonal symmetry acting on each nearest-neighbor pair of layers. The detailed procedure depends on the specific symmetry types. We have successfully implemented the method in a number of examples in different spatial dimensions, with symmetries that are conventional, higher-form, subsystem, anomalous, nonabelian, or noninvertible. We hence conjecture the method to be very general. For example, from the subsystem symmetry of the $2d$ plaquette Ising model, we derive the X-cube model and also an anisotropic fracton topological order. Additionally, starting from an anomalous $\mathbb Z_2$ symmetry in $1d$, we construct a new square lattice model realizing the double semion topological order.