Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-06-02
Europhys.Lett.92:57003,2010
Physics
Condensed Matter
Strongly Correlated Electrons
5 pages, no figures
Scientific paper
10.1209/0295-5075/92/57003
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 (or lack of) of topological defects. We concentrate on the (2+1)-dimensional case where the BF model reduce to a mixed Chern-Simons term and we show that the superconducting phase has a ground state degeneracy $k$ and not $k^2$. When the symmetry is $U(1) \times U(1)$, namely when both gauge fields are compact, this model is not equivalent to the sum of two Chern-Simons term with opposite chirality, even if naively diagonalizable. This is due to the fact that U(1) symmetry requires an ultraviolet regularization that make the diagonalization impossible. This can be clearly seen using a lattice regularization, where the gauge fields become angular variables. Moreover we will show that the phase in which both gauge fields are compact is not allowed dynamically.
Diamantini Cristina M.
Sodano Pasquale
Trugenberger Carlo A.
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