The Ashkin-Teller quantum chain and conformal invariance

Abstract

The authors study the finite-size effects for the fourth-state one-dimensional quantum chain introduced by Kohmoto et al. (1981) using different boundary conditions. From the corrections to the ground-state energy for periodic boundary conditions they verify that the central charge of the Virasoro algebra is equal to one in the whole domain of criticality. Their numerical study suggests a new relation between the corrections to the ground-state energy with free boundary conditions and with periodic boundary conditions. Various critical exponents including the surface ones and those corresponding to the para-fermions are determined.