A new correlator in quantum spin chains.pdfVIP

6 0 A new correlator in quantum spin chains 0 2 r J.P. Keating, F. Mezzadri and M. Novaes p School of Mathematics, University of Bristol, Bristol BS8 1TW, UK A 6 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 l probability that the first n spins of the chain are all aligned downwards. In e the s−EFP we let the spins in question be separated by s sites. The usual EFP - r corresponds to the special case when s = 1, and taking s 1 allows us to quantify t non-local correlations. We express the s−EFP for the anisotropic XY model in s . a transverse magnetic field, a system with both critical and non-critical regimes, t in terms of a Toeplitz determinant. For the isotropic XY model we find that the a m magnetic field induces an interesting length scale. - d n PACS numbers: 75.10.Pq, 02.30.Ik, 73.43.Nq o c [ 1. Introduction 1 The Emptiness Formation Probability (EFP) is defined for a one-dimensional spin-1/2 v 3 chain to be the probability of formation of a ferromagnetic string, i.e. the probability 7 that the first n spins of the chain are all aligned downwards, 1 P (n) = Z −1Tr{e−H/kBT F }, (1) 4