Topological defect network representations of fracton stabilizer codes

TL;DR

This paper introduces a systematic method to construct topological defect network representations for a broad class of fracton stabilizer codes, enabling new insights into their topological phases.

Contribution

It provides a general procedure to generate TDNs from lattice Hamiltonians, including models previously lacking such constructions, like Haah's cubic code.

Findings

Constructed TDNs for Haah's cubic code and fractal spin liquids.

Extended TDN construction to non-CSS models like Chamon's model.

Demonstrated the method's applicability to a wide range of fracton models.

Abstract

A topological defect network (TDN) is formed by a network of topological defects embedded within a topological quantum field theory (TQFT). TDNs were introduced recently for the purpose of describing fracton topological phases of matter using the framework of defect TQFT. Their effectiveness has been demonstrated through numerous examples, yet a systematic construction was lacking. Here we solve this problem by formulating a method to construct TDNs for a wide range of lattice Hamiltonians. Our method takes a lattice Hamiltonian as input, applies an ungauging procedure, then creates a refined lattice within each unit cell, followed by regauging the system to produce a TDN as output. For topological Calderbank-Shor-Steane (CSS) Pauli stabilizer models, this procedure is guaranteed to produce a phase equivalent TDN. This provides TDN representations of canonical fracton models for which no such construction was previously known, including Haah's cubic code and Yoshida's infinite family of fractal spin liquid models. We demonstrate the applicability of our method beyond CSS stabilizer models by constructing TDNs for non-CSS models including Chamon's model and the semionic X-cube model.