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arXiv:hep-th/9706061 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Finite size corrections in the massive Thirring model

T. Fujita, H. Takahashi

Published Sep 15, 1998• 2 citations
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Abstract

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 $1/L$ 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.

DOI
10.1103/physrevd.58.085011

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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 g0=\ensuremath−\ensuremathπ/4{g}_{0}=\ensuremath{-}\ensuremath{\pi}/4g0​=\ensuremath−\ensuremathπ/4 and decreases down to zero when g0=\ensuremath−\ensuremathπ/3.{g}_{0}=\ensuremath{-}\ensuremath{\pi}/3.g0​=\ensuremath−\ensuremathπ/3. This is quite different from the predicted central charge of the sine-Gordon model as well as the light cone six vertex model.
We discuss the bound states of the massive Thirring model. Here, the periodic boundary condition equations for the Bethe ansatz solutions are numerically solved. It is found that the massive Thirring model has only one bound state and the bound state spectrum as the function of the coupling constant agrees with that of infinite momentum frame prescription by Fujita and Ogura. Boson boson states (2p$-$2h states) appear only as the continuum spectrum without making any bound states. Further, the finite size correction to the vacuum energy is estimated. The evaluated central charge is found to be close to unity.
Recently Haldane has derived the Bethe ansatz equations describing the ground state properties of the massive Thirring model with finite `hole' density (the quantum sine-Gordon model with finite soliton density). His derivation is explicitly confirmed here using a particular cutoff scheme, and his solutions of the equations in various limits are reviewed with complementary results. The commensurate-incommensurate transition in the two-dimensional sine-Gordon model with a uniaxial misfit is examined at finite temperatures using the results obtained in the massive Thirring model.
The Hamiltonian of the massive Thirring model is explicitly diagonalized by formulating a Bethe ansatz for the eigenstates. The physical states are described by many-body wave functions representing the vacuum as a filled Fermi-Dirac sea and particle states as excitations built upon it. The spectrum of states is determined by imposing periodic boundary conditions on the wave functions. The energies are calculated by reducing the periodic boundary conditions to linear integral equations. For fermion-antifermion bound states the Dashen-Hasslacher-Neven spectrum is obtained. It is shown that the solution to the massive Thirring model can be understood as the critical limit of Baxter's solution of the eight-vertex model.
For the quantum sine-Gordon--massive Thirring model at finite temperature, the relationship between the Bethe ansatz ``elementary excitations'' and physical excitations of the system is examined. The thermodynamic equations are written in terms of a set of dressed particles in the general case. We find that the recently predicted soliton mass discontinuity (on varying coupling strength at finite temperature) is not a real effect--the function exhibiting the discontinuity does not correspond to the mass of the soliton.