1996/10/31 by Doochul Kim · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/0305-4470/30/11/013
published as J. Phys. A 30 (1997) 3817 · Minor corrections only. 18 pages in RevTex, 2 PS figures
arxiv created 1996/10/31 · arxiv updated 2009/11/30
The Bethe ansatz equation is solved to obtain analytically the leading finite-size correction of the spectra of the asymmetric XXZ chain and the accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary at zero vertical field. The energy gaps scale with size N as N-1/2 and its amplitudes are obtained in terms of level-dependent scaling functions. Exactly on the phase boundary, the amplitudes are proportional to a sum of square-root of integers and an anomaly term. By summing over all low-lying levels, the partition functions are obtained explicitly. Similar analysis is performed also at the phase boundary of zero horizontal field in which case the energy gaps scale as N-2. The partition functions for this case are found to be that of a nonrelativistic free fermion system. From symmetry of the lattice model under π/2 rotation, several identities between the partition functions are found. The N-1/2 scaling at zero vertical field is interpreted as a feature arising from viewing the Pokrovsky-Talapov transition with the space and time coordinates interchanged.