Issue
EPL
Volume 84, Number 5, December 2008
Article Number 57002
Number of page(s) 6
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
DOI http://dx.doi.org/10.1209/0295-5075/84/57002
Published online 25 November 2008
EPL, 84 (2008) 57002
DOI: 10.1209/0295-5075/84/57002

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

Yue Yu1 and Ziqiang Wang2

1   Institute of Theoretical Physics, Chinese Academy of Sciences - P.O. Box 2735, Beijing 100080, China
2   Department of Physics, Boston College - Chestnut Hill, MA 02467, USA

yyu@itp.ac.cn

received 2 June 2008; accepted in final form 21 October 2008; published December 2008
published online 25 November 2008

Abstract
Motivated by the work of Kitaev, we construct an exactly soluble spin-$\frac{1}2 $ model on a 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 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\leftrightarrow {\Delta_{1y}\over \strut\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-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.

PACS
75.10.Jm - Quantized spin models .
03.67.Pp - Quantum error correction and other methods for protection against decoherence .
71.10.Pm - Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.).

© EPLA 2008