A new correlator in quantum spin chains

TL;DR

This paper introduces the s-Emptiness Formation Probability (s-EFP), a new non-local correlator in quantum spin chains, expressed via Toeplitz determinants, revealing magnetic field-induced length scales in the XY model.

Contribution

It proposes the s-EFP as a generalization of EFP, providing a new tool to quantify non-local correlations in quantum spin chains, with explicit formulas for the XY model.

Findings

s-EFP generalizes EFP to separated spins

Expressed s-EFP in terms of Toeplitz determinants

Magnetic field induces a length scale in the isotropic XY model

Abstract

We propose a new correlator in one-dimensional quantum spin chains, the $s-$Emptiness Formation Probability ($s-$EFP). This is a natural 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 $s=1$, and 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.