Dipolar BF theory and dipolar braiding statistics

TL;DR

This paper explores the dipolar BF theory, revealing unique dipolar braiding statistics and establishing its equivalence to rank-2 tensor BF theory, providing new insights into dipole symmetry and topological quasiparticle behavior.

Contribution

It introduces a dipolar BF theory formulation that explicitly incorporates dipole symmetry and clarifies its relation to rank-2 tensor BF theory, enhancing understanding of dipolar topological phases.

Findings

Dipolar braiding statistics depend on quasiparticle positions.

Dipole-like quasiparticles exhibit anyon-like braiding.

Dipolar BF theory is equivalent to rank-2 tensor BF theory.

Abstract

We analyze the recently proposed dipolar BF theory with couplings to charge and dipole currents. The quasiparticles of the theory are either charge-like or dipole-like, and the mutual braiding statistics between charge-like and dipole-like quasiparticles are dipolar, meaning that it depends on the position of the quasiparticle being encircled. The braiding statistics between two dipole-like quasiparticles is that of ordinary anyons. We further prove that the dipolar BF theory is equivalent to the rank-2 tensor BF theory developed earlier as an effective theory for the rank-2 toric code. Although the two theories are equivalent, the dipolar BF formulation embodies the dipole symmetry explicitly and gives a clean insight into the way the dipole symmetry manifests itself in various conservation laws and the dipolar braiding statistics.