Estimates of the ground-state eigenvalue of the two-dimensional spin-12X−Ymodel

Abstract

An estimate as well as upper and lower bounds are presented for the ground-state energy density per spin of the two-dimensional spin-$\frac{1}{2}$ $X-Y$ model on a square lattice. The energy density is estimated to be ${\epsilon }_0=-1.099\mathrm{}\pm 0.004$ and is bounded by $-1.12498\mathrm{}<~{\epsilon }_0<~-1.09440\mathrm{}$.