Anyonic order parameters for discrete gauge theories on the lattice

Details Anyonic order parameters for discrete gauge theories on the lattice Anyonic order parameters for discrete gauge theories on the lattice

2008-12-11

arxiv.org/abs/0812.2256v1

Annals Phys.324:1168-1175,2009

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

14 pages, 1 figure

Scientific paper

10.1016/j.aop.2009.01.002

We present a new family of gauge invariant non-local order parameters for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation theory of the quantum double D(H) of the finite group H. These combine magnetic flux-sector labeled by a conjugacy class with an electric representation of the centralizer subgroup that commutes with the flux. In particular cases like the trivial class for magnetic flux, or the trivial irrep for electric charge, these order parameters reduce to the familiar Wilson and the 't Hooft operators respectively. It is pointed out that these novel operators are crucial for probing the phase structure of a class of discrete lattice models we define, using Monte Carlo simulations.

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