A new correlator in quantum spin chains

Abstract

We propose a new correlator in one-dimensional quantum spin chains, the s-emptiness formation probability (s-EFP). This is a generalization of the emptiness formation probability (EFP), which is the probability that the first n spins of the chain are all aligned downwards. In the s-EFP we let the spins in question be separated by s sites. The usual EFP corresponds to the special case when s = 1. Taking s > 1 allows us to quantify non-local correlations. We express the s-EFP for the anisotropic XY model in a transverse magnetic field, a system with both critical and non-critical regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find that the magnetic field induces an interesting length scale.