An exactly soluble model with tunable p-wave paired fermion ground states

Motivated by the work of Kitaev, we construct an exactly soluble spin-1/2 model on a honeycomb lattice whose ground states are identical to Delta(1x)p(x) + Delta(1y)p(y) + i(Delta(2x)p(x) + Delta(2y)p(y))- 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 p(x) <-> Delta(1y)/Delta(1x)p(y). 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. Copyright (C) EPLA, 2008