Bethe Ansatz Cluster Expansion Method for Quantum Integrable Particle Systems

Abstract

Presented is a method, which we call Bethe ansatz cluster expansion (BACE) method, to investigate statistical mechanics of quantum integrable systems. By use of only the Bethe ansatz equation, n-particle partition functions are exactly calculated. From the expression for the partition function, the n-particle cluster integrals are derived. The results completely agree with those of the thermal Bethe ansatz (TBA) by Yang and Yang. Thus, the BACE method directly proves the validity of the TBA. Partition theory and graphical representation are used to make the presentation simple and transparent.