Gauging Defects in Quantum Spin Systems

TL;DR

This paper develops a dynamical theory of defects in quantum spin systems, extending to topologically ordered phases, and demonstrates its equivalence to the critical transverse Ising model.

Contribution

It introduces a kinematic and dynamical framework for defects in quantum spin systems, including topologically ordered phases, using generalized algebraic techniques.

Findings

Constructed a kinematic theory for an indefinite number of defects.

Incorporated defect mobility via a microscopic Hamiltonian.

Shown equivalence to the critical transverse Ising model.

Abstract

The goal of this work is to build a dynamical theory of defects for quantum spin systems. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by allowing the defects to become mobile via a microscopic Hamiltonian. This construction is extended to topologically ordered systems by restricting to the ground state eigenspace of Hamiltonians generalizing the golden chain. We illustrate the construction with the example of a spin chain with $\mathbf{Vec}(\mathbb{Z}/2\mathbb{Z})$ fusion rules, employing generalized tube algebra techniques to model the defects in the chain. The resulting dynamical defect model is equivalent to the critical transverse Ising model.