Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories

TL;DR

This paper explores a duality operation in (2+1)d abelian lattice gauge theories involving twisted gauging of symmetries, using tensor networks to realize condensation defects and analyze the interplay of boundary conditions and charge sectors.

Contribution

It introduces explicit lattice realizations of condensation defects and duality operators via tensor networks, revealing the structure of symmetry and duality in abelian lattice gauge theories.

Findings

Constructed lattice models of condensation defects.

Analyzed the interplay of boundary conditions and charge sectors.

Identified 2-group symmetry structures in self-dual theories.

Abstract

Given a two-dimensional quantum lattice model with an abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a twisted way via a choice of discrete torsion. Using tensor networks, we introduce explicit lattice realisations of the so-called condensation defects, which are obtained by gauging the 1-form symmetry along submanifolds of spacetime, and employ the same calculus to realise the duality operators. By leveraging these tensor network operators, we compute the non-trivial interplay between symmetry-twisted boundary conditions and charge sectors under the duality operation, enabling us to construct isometries relating the dual Hamiltonians. Whenever a lattice gauge theory is left invariant under the duality operation, we explore the possibility of promoting the self-duality to an internal symmetry. We argue that this results in a symmetry structure that encodes the 2-representations of a 2-group.