Functional representations for correlators of spin chains

Herman E. Boos, M. Jimbo, T. Miwa +2 more

Michio Jimbo

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.

Gerhard Müller, H. Beck

David Pérez-Garcı́a, Miguel Tierz

Abstract. We construct a one-dimensional (1D) spin chain Hamiltonian with generic interactions and prove that the thermal correlation functions of the model admit an explicit random matrix representation. As an application of the result, we show how the observables of U ( N ) Chern–Simons theory on S 3 can be reproduced with the thermal correlation functions of the 1D spin chain, which is of the XX type, with a suitable choice of exponentially decaying interactions between infinitely many neighbours. We show that for this model, the correlation functions of the spin chain at a finite temperature give the Chern–Simons partition function, quantum dimensions and the full topological S -matrix.

N Kitanine, Jean Michel Maillet, N A Slavnov +1 more

We obtain a new multiple integral representation for the spin–spin correlation functions of the XXZ spin- infinite chain. We show that this representation is closely related with the partition function of the six-vertex model with domain wall boundary conditions.