arXiv:2005.09268 · Nuclear Physics B

Correlation functions of integrable O(n) spin chains

G A P Ribeiro

Published Jul 8, 2020• 11 citations

Abstract

We study the correlation functions of the integrable O(n) spin chain in the thermodynamic limit. We addressed the problem of solving functional equations of the quantum Knizhnik Zamolodchikov type for density matrix related to the O(n) spin chain. We give the explicit solution for two-sites density matrix elements for the O(n) which are then evaluated for the n=3,4,…,8 cases at zero temperature.

DOI: 10.1016/j.nuclphysb.2020.115106

Related papers

Correlation functions of the integrable spin- s chain ∗

G A P Ribeiro, Andreas Klümper

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.

arXiv:1603.00504Journal of Physics A Mathematical and TheoreticalMay 12, 201611 citations

Correlation functions of the integrable S U ( n ) spin chain

G A P Ribeiro, Andreas Klümper

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.

arXiv:1804.10169Journal of Statistical Mechanics Theory and ExperimentJan 1, 201920 citations

Correlation functions of the integrable isotropic spin-1 chain: algebraic expressions for arbitrary temperature

Andreas Klümper, Dominic Nawrath, Junji Suzuki

We derive algebraic formulae for the density matrices of finite segments of the integrable s u (2) isotropic spin-1 chain in the thermodynamic limit. We give explicit results for the 2- and 3-site cases for arbitrary temperature T and zero field. In the zero-temperature limit the correlation functions are given in elementary form in terms of Riemann's zeta function at even integer arguments.

arXiv:1304.5512Journal of Statistical Mechanics Theory and ExperimentAug 27, 201317 citations

Correlation functions of the higher spinXXXchains

N Kitanine

Using the algebraic Bethe ansatz, we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin ½ Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can be considered in the framework of this approach in the thermodynamic limit. Finally, a multiple integral representation for the spin 1 zero-temperature correlation functions is obtained in the thermodynamic limit.

arXiv:math-ph/0104016Journal of Physics A Mathematical and GeneralSep 21, 200141 citations

Reduced qKZ equation: general case

Klümper, A., Nirov, K., Razumov, A.

We use the quantum group approach for the investigation of correlation functions of integrable vertex models and spin chains. For the inhomogeneous reduced density matrix in case of an arbitrary simple Lie algebra we find functional equations of the form of the reduced quantum Knizhnik-Zamolodchikov equation. This equation is the starting point for the investigation of correlation functions at arbitrary temperature and notably for the ground state.

Jan 1, 20206 citations

Reduced qKZ equation: general case

Andreas Klümper, Khazret S Nirov, Alexander V Razumov

Abstract We use the quantum group approach for the investigation of correlation func- tions of integrable vertex models and spin chains. For the inhomogeneous reduced density matrix in case of an arbitrary simple Lie algebra we find functional equations of the form of the reduced quantum Knizhnik–Zamolodchikov equation. This equation is the starting point for the investigation of correlation functions at arbitrary temperature and notably for the ground state.

arXiv:1905.06014Journal of Physics A Mathematical and TheoreticalAug 15, 20198 citations