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Physical Review Letters

Factorized S -Matrix Method for the Thermodynamics of the Massive Thirring Model

S. G. Chung, Yoshi Oono, Yia‐Chung Chang

Published Jul 25, 1983• 9 citations
Publisher

Abstract

A new method based on the $S$-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.

DOI
10.1103/physrevlett.51.241

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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.
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.
We calculate for the first time the finite size corrections in the massive Thirring model. This is done by numerically solving the equations of periodic boundary conditions of the Bethe ansatz solution. It is found that the corresponding central charge extracted from the 1/L1/L1/L term is around 0.4 for the coupling constant of ${g}_{0}=\ensuremath{-}\ensuremath{\pi}/4$ and decreases down to zero when ${g}_{0}=\ensuremath{-}\ensuremath{\pi}/3.$ This is quite different from the predicted central charge of the sine-Gordon model as well as the light cone six vertex model.
This paper determines the zero-temperature equation of state for the massive Thirring / sine-Gordon model. This demonstrates recently derived model-independent upper and lower bounds on the zero-temperature equation of state with fixed number density from systems with a nonzero current density. That approach is potentially valuable as Monte Carlo calculations with a current density avoid the sign problem in the Euclidean formulation. An advantage to illustrating these bounds in the massive Thirring/sine-Gordon model is that the relevant calculations with both a number density and a current density can be done using a Bethe ansatz. For this model, optimal bounds constrain the energy density as a function of number density by a factor of two from above and below at high densities for all choices of couplings. The lower bound becomes exact at low densities, while the upper bound approaches the worst constraint of a factor of 4.90 .