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arXiv:math-ph/0111031 · Journal of Physics A Mathematical and General

LocalU(1) symmetry inY(SO(5)) associated with the massless Thirring model and its Bethe ansatz

Hongbiao Zhang, Mo‐Lin Ge, Kang Xue

Published Sep 6, 2000• 0 citations
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Abstract

The massless Thirring model associated with SO (5) is solved in terms of the local U (1) symmetry. The local U (1) symmetry is related to q-deformation of four-component field operators due to the nonlinear interaction for different internal degrees of freedom. The Bethe ansatz wavefunction is also discussed. In addition, the local U (1) symmetry in the Yangian associated with SO (5)( Y ( SO (5))) is explored.

DOI
10.1088/0305-4470/33/37/101

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The massless Thirring model associated with SO (5) is solved in terms of the local U (1) symmetry. The local U (1) symmetry is related to q-deformation of four-component field operators due to the nonlinear interaction for different internal degrees of freedom. The Bethe ansatz wavefunction is also discussed. In addition, the local U (1) symmetry in the Yangian associated with SO (5)( Y ( SO (5))) is explored.
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 study Olshanski twisted Yangian based models, known as one-dimensional “soliton non-preserving” open spin chains, by means of algebraic Bethe Ansatz. The even case, when the bulk symmetry is \mathfrak{gl}_{2n} 𝔤 𝔩 2 n and the boundary symmetry is \mathfrak{sp}_{2n} 𝔰 𝔭 2 n or \mathfrak{so}_{2n} 𝔰 𝔬 2 n , was studied in [Ann. Henri Poincaré 20, 339 (2018)]. In the present work, we focus on the odd case, when the bulk symmetry is \mathfrak{gl}_{2n+1} 𝔤 𝔩 2 n + 1 and the boundary symmetry is \mathfrak{so}_{2n+1} 𝔰 𝔬 2 n + 1 . We explicitly construct Bethe vectors and present a more symmetric form of the trace formula. We use the composite model approach and Y(\mathfrak{gl}_n) Y ( 𝔤 𝔩 n ) -type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.