Exact thermodynamics of the Hubbard chain: free energy and correlation lengths

Andreas Kl�mper, Christian Scheeren

U. Brandt

Gregory S. Um, P. J. Gambardella, Max Dresden

We propose a generalized compressible Ising model and solve it exactly, using the renormalization-group method. We obtain exact expressions for free energy and spin-spin correlation functions for periodic and free boundary condition in a finite chain or in the thermodynamic limit. Through this method, we develop functional recursion relations. The corresponding fixed points are investigated with the correlation length. Our method is applicable to higher-order correlation functions.

Minoru Takahashi

Andreas Klümper, Christian Scheeren

This chapter reviews the various techniques developed for the study of the thermodynamics of integrable systems at the example of the simplest one, namely the spin-12 Heisenberg chain. As a matter of fact, the strict ground state is inaccessible due to the very fundamentals of thermodynamics. The minimization of the free energy functional yields what is known as the thermodynamical Bethe ansatz. Application of thermodynamical data of quantum spin chains is the microscopic modelling of magnetic systems such as spin-Peierls compounds and ladder systems. The microscopic interactions of a given substance are determined by a comparative analysis of the experimental results for the susceptibility and the theoretical data obtained for a model. Lowering the temperature, the systems enter a large regime with non-universal correlations and finally approach the quantum critical point at exactly zero temperature showing again universal yet nontrivial properties with divergent correlation lengths governed by conformal field theory.

D. Grensing, Heinz Koppe