Spin–spin correlation in some excited states of the transverse Ising model
Journal of Physics A: Mathematical and Theoretical
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 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 Fisher-Hartwig conjecture. The result is that
... he result is that the correlation decays algebraically with distance ($n$) as $1/\surd n$ and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.