Topological quantum phase transitions in topological superconductors

¹ INFN and Dipartimento di Fisica, University of Perugia - via A. Pascoli, I-06100 Perugia, Italy, EU
² SwissScientifique - ch. Diodati 10, CH-1223 Cologny, Switzerland

^a cristina.diamantini@pg.infn.it
^b pasquale.sodano@pg.infn.it
^c ca.trugenberger@bluewin.ch

Received: 2 June 2010
Accepted: 8 November 2010

Abstract

In this paper we show that BF topological superconductors (insulators) exibit phase transitions between different topologically ordered phases characterized by different ground-state degeneracy on manifold with non-trivial topology. These phase transitions are induced by the condensation of (or lack of) topological defects. We concentrate on the (2+1)-dimensional case where the BF model reduces to a mixed Chern-Simons term and we show that the superconducting phase has a ground-state degeneracy k and not k². When the symmetry is U(1)×U(1), namely when both gauge fields are compact, the mixed Chern-Simons model is not equivalent to the sum of two Chern-Simons terms with opposite chirality (even if naively diagonalizable) since the U(1) symmetry requires an ultraviolet regularization that makes the diagonalization impossible. We analyze this aspect using a lattice regularization, where the gauge fields become angular variables. In addition, we will show that the phase in which both gauge fields are compact is not allowed dynamically.