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arXiv:hep-th/0410221 · Journal of the Physical Society of Japan

New Vacuum of Bethe Ansatz Solutions in Thirring Model

Takehisa Fujita, Makoto Hiramoto, Takeshi Homma, Hidenori Takahashi

Published Apr 1, 2005• 10 citations
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Abstract

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 ($1p-1h$) states, and find that it has a finite gap. The analytical expressions for the true vacuum as well as for the lowest $1p-1h$ 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.

DOI
10.1143/jpsj.74.1143

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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 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.
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.
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.
Bariev's model for correlated hopping in one dimension is integrable and soluble within the framework of two nested Bethe Ansätze. For repulsive interaction and finite magnetization the low energy excitation spectrum is a two-component Luttinger liquid with conformal charges c=1. In zero magnetic field the spectrum of spin excitations is gapped. For higher energy excitations the single-hole (single-particle) spectral functions display edge singularities that deviate from those expected from a Luttinger liquid. The system can be described as a mobile impurity coupled to the Luttinger liquid yielding an effective x-ray edge type model. Using the Bethe Ansatz solution for repulsive interaction we obtain expressions for the critical exponents for the single-particle and single-hole Green's functions in zero magnetic field.