English

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

Strongly Correlated Electrons 2009-11-13 v3 Mesoscale and Nanoscale Physics

Abstract

Motivated by the work of Kitaev, we construct an exactly soluble spin-12\frac{1}2 model on honeycomb lattice whose ground states are identical to Δ1xpx+Δ1ypy+i(Δ2xpx+Δ2ypy)\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 pxΔ1yΔ1xpyp_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=1/2c=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.

Keywords

Cite

@article{arxiv.0708.0631,
  title  = {An exactly soluble model with tunable p-wave paired fermion ground states},
  author = {Yue Yu and Ziqiang Wang},
  journal= {arXiv preprint arXiv:0708.0631},
  year   = {2009}
}

Comments

6 pages, 2 figures, published version