Spin–spin correlation in some excited states of the transverse Ising model

Abstract

We consider the transverse Ising model in one dimension with nearest neighbour interaction and calculate exactly the longitudinal spin–spin correlation for a class of excited states. These states are known to play an important role in the perturbative treatment of the one-dimensional transverse Ising model with frustrated second-neighbour interaction. To calculate the correlation, we follow the earlier procedure of Wu, use Szego's theorem and also use the Fisher–Hartwig conjecture. The result is that the correlation decays algebraically with distance (n) as 1/√n and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.