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

Motivated by the work of Kitaev, we construct an exactly soluble spin-½ model on a honeycomb lattice whose ground states are identical to Δ_1xp_x+Δ_1yp_y+i(Δ_2xp_x+Δ_2yp_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 ↔ (Δ_1y / Δ_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.