Abstract
Jesper Romers (University of Amsterdam, the Netherlands)
The modular S-matrix as an order parameter for topological phase transitions
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 S-matrix, also in the
broken phase. From the measured broken S-matrix 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 S-matrix can be
employed as a matrix valued non-local order parameter from which the
low-energy effective theories that occur in different regions of parameter
space can be fully determined.
To verify our predictions we studied a non-abelian anyon model based on
the quaternion group of order 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.