String and Membrane condensation on 3D lattices

TL;DR

This paper explores the properties of 3D lattice spin models with string and membrane condensates, revealing new topological orders and behaviors of excitations in exactly solvable models.

Contribution

It introduces three exactly solvable 3D spin models with string and membrane condensates, demonstrating novel topological orders and excitation properties.

Findings

Models exhibit topological order at low energies

Open-string ends behave as fermions or bosons depending on the model

New type of topological order identified in the third model

Abstract

In this paper, we investigate the general properties of lattice spin models that have string and/or membrane condensed ground states. We discuss the properties needed to define a string or membrane operator. We study three 3D spin models which lead to Z_2 gauge theory at low energies. All the three models are exactly soluble and produce topologically ordered ground states. The first model contains both closed-string and closed-membrane condensations. The second model contains closed-string condensation only. The ends of open-strings behave like fermionic particles. The third model also has condensations of closed membranes and closed strings. The ends of open strings are bosonic while the edges of open membranes are fermionic. The third model contains a new type of topological order.