Dipolar BF theory and dipolar braiding statistics
arxiv(2024)
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.
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