The modular Smatrix as order parameter for topological phase transitions
Abstract
We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To probe the phase structure we use a complete set of open and closed anyonic string operators. The open strings allow one to determine the particle content of the condensate, whereas the closed strings enable us to determine the matrix elements of the modular Smatrix, in both the unbroken and broken phases. From the measured broken Smatrix we may read off the sectors that split or get identified in the broken phase, as well as the sectors that are confined. In this sense the modular Smatrix can be employed as a matrix valued nonlocal order parameter from which the lowenergy effective theories that occur in different regions of parameter space can be fully determined. To verify our predictions, we studied a nonabelian anyon model based on the quaternion group H=\skew3\bar {D_2} of the order of eight by Monte Carlo simulation. We probe part of the phase diagram for the pure gauge theory and find a variety of phases with magnetic condensates leading to various forms of (partial) confinement in complete agreement with the algebraic breaking analysis. Also the order of various transitions is established.
 Publication:

New Journal of Physics
 Pub Date:
 March 2012
 DOI:
 10.1088/13672630/14/3/035024
 arXiv:
 arXiv:1108.0683
 Bibcode:
 2012NJPh...14c5024B
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 37 pages