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arXiv:hep-th/9609224

Bound states of 1+1 dimensional field theories

Takehisa Fujita, Makoto Hiramoto, Hidenori Takahashi

Published Sep 28, 1996• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.hep-th/9609224

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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.
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.
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.
We find a new vacuum of the Bethe ansatz solutions in the massless Thirring model. This vacuum breaks the chiral symmetry and has the lower energy than the well-known symmetric vacuum energy. Further, we evaluate the energy spectrum of the one particle-one hole (1p−1h1p-1h1p−1h) states, and find that it has a finite gap. The analytical expressions for the true vacuum as well as for the lowest 1p−1h1p-1h1p−1h excited state are also found. Further, we examine the bosonization of the massless Thirring model and prove that the well-known procedure of bosonization of the massless Thirring model is incomplete because of the lack of the zero mode in the boson field.
We use the Bethe ansatz solution for the one-dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials, one finds that the true ground state contains a single charge or, for boundary potentials comparable with the Hubbard interaction, a pair of electrons in a bound state. If these are left unoccupied one finds holon and spinon bound states. We compute the finite size corrections to the low-lying energies in this system and use the predictions of boundary conformal field theory to study the exponents related to the orthogonality catastrophe.
We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one finds that the true ground state contains a single charge or, for boundary potentials comparable to the Hubbard interaction, a pair of electrons in a bound state. If these are left unoccupied one finds holon and spinon bound states. We compute the finite size corrections to the low lying energies in this system and use the predictions of boundary conformal field theory to study the exponents related to the orthogonality catastrophe.
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.