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Abstract:

We studied charged excitations of the ν=5/2 fractional quantum Hall state allowing for spin depolarization. It is generally accepted that the ground state is a spin-polarized incompressible quantum liquid, adiabatically connected to the Pfaffian state, whose spin-polarized quasiholes (QHs) obey non-Abelian statistics. Using numerical diagonalization and taking account of non-zero well widths we demonstrated that at a sufficiently low Zeeman energy it is energetically favorable for pairs of charge e/4 QHs to bind into charge e/2 Skyrmions. We showed that Skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized ground state in realistic experimental situations. © 2011 American Institute of Physics.

Abstract:

We describe a family of phase transitions connecting phases of differing nontrivial topological order by explicitly constructing Hamiltonians of the Levin-Wen type which can be tuned between two solvable points, each of which realizes a different topologically ordered phase. We show that the low-energy degrees of freedom near the phase transition can be mapped onto those of a Potts model, and we discuss the stability of the resulting phase diagram to small perturbations about the model. We further explain how the excitations in the condensed phase are formed from those in the original topological theory, some of which are split into multiple components by condensation, and we discuss the implications of our results for understanding the nature of general achiral topological phases in 2 + 1 dimensions in terms of doubled Chern-Simons theories. © 2011 American Physical Society.