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Physical review. B, Condensed matter

Bethe-ansatz massive-Thirring-model thermodynamics: The weak-coupling limit

X. Zotos

Published Sep 1, 1982• 14 citations
Publisher

Abstract

Using the Bethe-ansatz method we analyze the thermodynamic properties of the massive Thirring model in the zero-charge-sector attractive case, including the "charged vacuum" excitations introduced by Korepin. The energy of these excitations is calculated as a function of momentum and temperature and agrees with Korepin's results at $T=0$. The specific heat is presented and shown to vary smoothly for the whole range of coupling in the attractive regime.

DOI
10.1103/physrevb.26.2519

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Journal of Physics C Solid State Physics•Jan 10, 1983•27 citations
Using the Bethe-ansatz method we analyze the thermodynamic properties of the massive Thirring model in the zero-charge-sector attractive case, including the "charged vacuum" excitations introduced by Korepin. The energy of these excitations is calculated as a function of momentum and temperature and agrees with Korepin's results at T=0T=0T=0. The specific heat is presented and shown to vary smoothly for the whole range of coupling in the attractive regime.
A new method based on the SSS-matrix factorization is developed for the thermodynamics of the massive Thirring model. The method can be applied to any charge sector and coupling constant. In the zero-charge sector, the present theory reproduces all the Bethe-Ansatz-theory results in the attractive-coupling regime, and agrees with a perturbation calculation in the repulsive-coupling regime.
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 $\frac{\ensuremath{\mu}}{\ensuremath{\pi}}$ these reduce to a finite set, solved here numerically for $\ensuremath{\mu}=[\frac{(n\ensuremath{-}1)}{n}]\ensuremath{\pi}$, for several values of nnn, to give the specific heat as a function of temperature. The "soliton" contribution peaks at $\ensuremath{\simeq}0.4$ soliton masses for $\ensuremath{\mu}=\frac{4}{5}\ensuremath{\pi}$, shifting downward for higher $\ensuremath{\mu}$. A detailed analysis of the sine-Gordon limit of the XYZ\mathrm{XYZ}XYZ spin chain is presented, and a non-Lorentz-invariant feature of that limit is noted.
The thermodynamics of the massive Thirring model is discussed with the help of the Bethe Ansatz approach in a way different from Fowler and Zotos (1982). In particular a finite Debye cut-off is introduced to investigate effects of the lattice discreteness. The specific heat seems to have a structure as a sum of the Debye-type specific heat and a 'soliton' peak, when the authors take into account the relation of the massive Thirring model to the quantum sine-Gordon model. The finite temperature excitations are calculated. The excitation energy proposed by Fowler and Zotos is shown to have significance which is insensitive to the way of formulation.