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A LOCAL AND INTEGRABLE LATTICE REGULARIZATION OF THE MASSIVE THIRRING MODEL

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

The light–cone lattice approach to the massive Thirring model is reformulated using a local and integrable lattice Hamiltonian written in terms of discrete fermi fields. Several subtle points concerning boundary conditions, normal–ordering, continuum limit, finite renormalizations and decoupling of fermion doublers are elucidated. The relations connecting the six–vertex anisotropy and the various coupling constants of the continuum are analyzed in detail. IFUM–510–FT

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The light–cone lattice approach to the massive Thirring model is reformulated using a local and integrable lattice Hamiltonian written in terms of discrete fermi fields. Several subtle points concerning boundary conditions, normal–ordering, continuum limit, finite renormalizations and decoupling of fermion doublers are elucidated. The relations connecting the six–vertex anisotropy and the various coupling constants of the continuum are analyzed in detail. IFUM–510–FT
The continuous limit of the eight-vertex model is shown to give solely the Massive Thirring Model (MTM). More precisely, using the light-cone lattice approach we find a whole class of lattice spacing (a) dependences in the eight vertex parameters (θ, γ, k) yielding a relative field theory in the a=0 limit. This turns out to be the MTM with no dependence on k. The exact excitation spectrum calculation presented here lead to these conclusions. Analogous results are reached from a perturbative renormalization group study of the anisotropic current-current continuum fermion field theory.
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 6-vertex model with appropriately chosen alternating inhomogeneities gives the so-called light-cone lattice regularization of the sine-Gordon (Massive-Thirring) model. In this integrable lattice model we consider pure hole states above the antiferromagnetic vacuum and express the norm of Bethe-wave functions in terms of the hole's positions and the counting-function of the state under consideration. In the light-cone regularized picture pure hole states correspond to pure soliton (fermion) states of the sine-Gordon (massive Thirring) model. Hence, we analyze the continuum limit of our new formula for the norm of the Bethe-wave functions. We show, that the physically most relevant determinant part of our formula can be expanded in the large volume limit and turns out to be proportional to the Gaudin-determinant of pure soliton states in the sine-Gordon model defined in finite volume.
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.
The light-cone approach is reviewed. This method allows to find the underlying quantum field theory for any integrable lattice model in its gapless regime. The relativistic spectrum and S-matrix follows straightforwardly in this way through the Bethe Ansatz. We show here how to derive the infinite number of local commuting and non-local and non-commuting conserved charges in integrable QFT, taking the massive Thirring model (sine-Gordon) as an example. They are generated by quantum monodromy operators and provide a representation of q−q-q−deformed affine Lie algebras $U_q({\hat\G})$. Based on lectures delivered at the XXXqXXX_qXXXq​ Karpacz Winter School, Poland, February 14-26, 1994.
The exact solution of the A (2) n integrable lattice models is presented. The free energy and excitation energies of the vertex models are found as functions of the spectral and anisotropy parameters as well as the finite-size corrections yielding the central charges and conformal dimensions. These lattice models yield a new massive QFT where the mass spectrum and the S-matrix are obtained through the light-cone approach. The ground state and excitation energies of a new anisotropic spin-one integrable chain associated to the A (2) 2 model are computed.