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

Abstract

Motivated by the work of Kitaev, we construct an exactly soluble spin-$\frac{1}{2}$ model on 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 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 $p_x\leftrightarrow \frac{{\Delta }_{1y}}{{\Delta }_{1x}}{p}_y$. The G-inversion symmetric gapless B phase near the phase boundaries is described by 1+1-dimensional gapless Majorana fermions in the asymptotic long wave length 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.

6 pages, 2 figures, published version

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• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
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