Quantum spin chain, Toeplitz determinants and the Fisher-Hartwig conjecture

Abstract

We consider the one-dimensional quantum spin chain, which is called the XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We are mainly interested in the entropy of a block of L neighboring spins at zero temperature and of an infinite system. We represent the entropy in terms of a Toeplitz determinant and calculate the asymptotic analytically. We derive the first two terms of the asymptotic decomposition. Interestingly, these two terms of decomposition clearly show a length scale related to the field h.