An exactly soluble model with tunable p-wave paired fermion ground statesYue Yu1 and Ziqiang Wang2
1 Institute of Theoretical Physics, Chinese Academy of Sciences - P.O. Box 2735, Beijing 100080, China
2 Department of Physics, Boston College - Chestnut Hill, MA 02467, USA
received 2 June 2008; accepted in final form 21 October 2008; published December 2008
published online 25 November 2008
Motivated by the work of Kitaev, we construct an exactly soluble spin- model on a honeycomb lattice whose ground states are identical to -wave paired fermions on a square lattice, with tunable paring order parameters. We derive a universal phase diagram for this general p-wave theory which contains a gapped A-phase and a topologically non-trivial B-phase. We show that the gapless condition in the B-phase is governed by a generalized inversion (G-inversion) symmetry under . The G-inversion symmetric gapless B-phase near the phase boundaries is described by (1+1)-dimensional gapless Majorana fermions in the asymptotic long-wavelength limit, i.e. the c = 1/2 conformal field theory. The gapped B-phase has G-inversion symmetry breaking and is the weak pairing phase described by the Moore-Read Pfaffian. We show that in the gapped B-phase, vortex pair excitations are separated from the ground state by a finite energy gap.
75.10.Jm - Quantized spin models .
03.67.Pp - Quantum error correction and other methods for protection against decoherence .
71.10.Pm - Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.).
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