Coherent Anomaly in Kosterlitz-Thouless-Type Transition in the S=1⁄2 XXZ Chain at the Ground State

Abstract

A Kosterlitz-Thouless (KT)-type transition in the one-dimensional S=1⁄2 XXZ model at the ground state is analyzed using the double-cluster approximation (DCA) and the coherent-anomaly method (CAM). It is numerically shown that the periodic-boundary condition (PBC) is suitable for the construction of a systematic series of cluster approximations in quantum antiferromagnets. The transition point and the exponent of the essential singularity are estimated as g_c^*\simeq0.9969 and σ\simeq0.527, which are in good agreement with the exact values, g_c^*=1 and σ=0.5, respectively. Such accuracy of estimation is due to the consideration of a power-law factor in front of the exponential singularity of \barχ, which had been neglected until now.