p波成对费米子基态可调的精确可解模型
An exactly soluble model with tunable p-wave paired fermion ground states
摘要：
受Kitaev工作的启发，我们构造了一个精确可解的蜂窝格子上的自旋$\frac{1}2$模型，它的基态与正方格子上的$Δ_{1x}p_x+Δ_{1y}p_y+i(Δ_{2x}p_x+Δ_{2y}p_y)$ -波配对费米子完全相同，且配对序参量可调.我们推导出一个通用的相图，这个一般的p波理论，其中包含一个缺口的A相和拓扑非平凡的B相。我们表明，在B相的无隙条件下是由广义反演（G-反演）对称性下$p_x\leftrightarrow {Δ_{1y}\over Δ_{1x}} p_y$。相界附近的G反转对称无带隙B相由1+1维无带隙的Majorana费米子在渐近长波极限下描述，即$c=1/2$共形场论。带隙的B相具有G-反转对称性破缺，并且是由Moore-Read Pfweian描述的弱配对相。我们发现，在带隙的B相，涡旋对激发分离的基态由一个有限的能隙。
英文摘要：
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 $Δ_{1x}p_x+Δ_{1y}p_y+i(Δ_{2x}p_x+Δ_{2y}p_y)$-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 $p_x\leftrightarrow {Δ_{1y}\over Δ_{1x}} p_y$. The G-inversion symmetric gapless B phase near the phase boundaries is described by 1+1-dimensional gapless Majorana fermions in the asymptotic long 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.
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