Bethe ansatz: Finite-temperature thermodynamics

Ladislav Šamaj, Zoltán Bajnok

X. Zotos

S. G. Chung

There exist some criticisms of the Bethe ansatz formulation predicting a discontinuity for the sine-Gordon soliton mass at finite temperatures. The basic ideas and some key steps of the Bethe ansatz thermodynamics are examined and clarified along with associated criticisms. The validity of the Bethe ansatz theory is demonstrated and an experimental implication is discussed.

Hans-Peter Eckle

Abstract This chapter discusses how the Bethe ansatz solution of the one-dimensional Bose gas with repulsive δ-function interaction is extended to finite temperatures, the thermody- namic Bethe ansatz. The excitations of this system consist of particle and hole excitations, which can be described by the corresponding densities of Bethe ansatz roots. It shows how these Bethe ansatz root densities are used to define an appropriate expression for the entropy of the system of Bose particles, which is the main ingredient for the extension of the Bethe ansatz method to finite temperature.

Horaƫiu Năstase

X. Zotos, Michael Fowler

The thermal renormalization of the Bethe-ansatz excitation spectrum for the sine-Gordon system is presented. For the soliton mass, the results agree closely with those of Maki and Takayama over a significant temperature range, but the sudden decrease in mass they predict near a particular temperature is not found. For the Bethe-ansatz excitation corresponding to the phonon at zero temperature, the rest mass changes rapidly as the temperature increases, even near the classical limit. This suggests that at finite temperature this excitation (the one-string) no longer corresponds to the physical phonon.