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

TL;DR

This paper introduces an exactly solvable spin-1/2 model on a honeycomb lattice with ground states equivalent to tunable p-wave paired fermions, revealing a universal phase diagram with topological phases and Majorana fermion excitations.

Contribution

It constructs a new exactly solvable model linking honeycomb spin systems to p-wave paired fermions with tunable parameters, and characterizes its phase diagram and topological properties.

Findings

Identifies a gapped A phase and a topologically non-trivial B phase.

Shows the B phase's gapless condition is governed by G-inversion symmetry.

Demonstrates the B phase hosts Majorana fermions and Moore-Read Pfaffian state.

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 $p_x\leftrightarrow {\Delta_{1y}\over \Delta_{1x}} p_y$. 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.