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arXiv:1603.00504 · Journal of Physics A Mathematical and Theoretical

Correlation functions of the integrable spin- s chain ∗

G A P Ribeiro, Andreas Klümper

Published May 12, 2016• 11 citations
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Abstract

Abstract We study the correlation functions of su (2) invariant spin- s chains in the thermodynamic limit. We derive nonlinear integral equations for an auxiliary correlation function ω for any spin s and finite temperature T . For the spin-3/2 chain for arbitrary temperature and zero magnetic field we obtain algebraic expressions for the reduced density matrix of two-sites. In the zero temperature limit, the density matrix elements are evaluated analytically and appear to be given in terms of Riemann’s zeta function values of even and odd arguments.

DOI
10.1088/1751-8113/49/25/254001

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Abstract We study the correlation functions of su (2) invariant spin- s chains in the thermodynamic limit. We derive nonlinear integral equations for an auxiliary correlation function ω for any spin s and finite temperature T . For the spin-3/2 chain for arbitrary temperature and zero magnetic field we obtain algebraic expressions for the reduced density matrix of two-sites. In the zero temperature limit, the density matrix elements are evaluated analytically and appear to be given in terms of Riemann’s zeta function values of even and odd arguments.
Abstract We study the correlation functions of , n > 2, invariant spin chains in the thermodynamic limit. We formulate a consistent framework for the computation of short-range correlation functions via functional equations which hold even at finite temperature. We give the explicit solution for two- and three-site correlations for the case at zero temperature. The correlators do not seem to be of factorizable form. From the two-site result we see that the correlation functions are given in terms of Hurwitz’s zeta function, which differs from the case where the correlations are expressed in terms of Riemann’s zeta function of odd arguments.
The calculation of the correlation functions of Bethe ansatz solvable models is very difficult problem.Among these solvable models spin 1/2 XXX chain has been investigated for a long time.Even for this model only the nearest neighbor and the second neighbor correlations were known.In 1990's multiple integral formula for the general correlations is derived.But the integration of this formula is also very difficult problem.Recently these integrals are decomposed to products of one dimensional integrals and at zero temperature, zero magnetic field and isotropic case, correlation functions are expressed by log 2 and Riemann's zeta functions with odd integer argument ζ(3), ζ(5), ζ(7), . . . .We can calculate density sub-matrix of successive seven sites.Entanglement entropy of seven sites is calculated.These methods can be extended to XXZ chain up to n = 4. Correlation functions are expressed by the generalized zeta functions.Several years ago I derived new thermodynamic Bethe ansatz equation for XXZ chain.This is quite different with Yang-Yang type TBA equations and contains only one unknown function.This equation is very useful to get the high temperature expansion.In this paper we get the analytic solution of this equation at ∆ = 0.