Bethe-ansatz quantum sine-Gordon thermodynamics. The specific heat

Abstract

The Bethe-ansatz equations for the thermodynamic properties of the quantum sine-Gordon systems are derived in the zero-charge-sector attractive case. For rational values of the coupling parameter $\frac{\mu }{\pi }$ these reduce to a finite set, solved here numerically for $\mu =\left[\frac{\mathrm{}(n-1\mathrm{})\mathrm{}}{n}\right]\pi$, for several values of $n$, to give the specific heat as a function of temperature. The "soliton" contribution peaks at $\simeq 0.4$ soliton masses for $\mu =\frac{4}{5}\pi$, shifting downward for higher $\mu$. A detailed analysis of the sine-Gordon limit of the $\mathrm{XYZ}$ spin chain is presented, and a non-Lorentz-invariant feature of that limit is noted.