aqora

24pT-7 On the non-regular Bethe states of XXX model and a new classification scheme of string solutions

哲生出口

日本物理学会講演概要集Sep 3, 19990 citations

Solutions of the Bethe Equations for the XXZ Model

V. Tarasov

Journal of Mathematical SciencesDec 4, 20040 citations

Violations of the string hypothesis in the solutions of the Bethe ansatz equations in the XXX-Heisenberg model

K. Isler, Manu B. Paranjape

arXiv:hep-th/9304078Physics Letters BDec 1, 199325 citations

Bethe-root configurations and spectral degeneracy in the open XXZ chain with degenerate boundaries

Shizhang Wu, Shu Chen, Junpeng Cao +1 more

We investigate the structure of Bethe-root configurations in the spin-1/2 XXZ chain with degenerate open boundaries. The physical solutions of the Bethe Ansatz equations are classified into three types in the fully degenerate case and two types in the partially degenerate case, for which we propose counting formulas for the number of physical solution sets of each type. Furthermore, we observe spectral degeneracies in the fully degenerate case and show that they can be naturally explained by the presence of specific phantom strings in the Bethe roots. The classification and resulting spectral degeneracies in the diagonal limit are also discussed.We investigate the structure of Bethe-root configurations in the spin-1/2 XXZ chain with degenerate open boundaries. The physical solutions of the Bethe Ansatz equations are classified into three types in the fully degenerate case and two types in the partially degenerate case, for which we propose counting formulas for the number of physical solution sets of each type. Furthermore, we observe spectral degeneracies in the fully degenerate case and show that they can be naturally explained by the presence of specific phantom strings in the Bethe roots. The classification and resulting spectral degeneracies in the diagonal limit are also discussed.

arXiv:2608.20815Aug 21, 20260 citations

New solutions of the Bethe ansatz equations for the isotropic and anisotropic spin-1/2Heisenberg chain

Guido Jüttner, B -D Dorfel

Bethe ansatz equations (BAE) are investigated for the isotropic spin- 1 / 2 Heisenberg chain as well as the XXZ chain with real solutions characterized by identical integers in the logarithmic form of the BAE. Such states do not belong to the usual classification scheme (string hypothesis). They always exist in critical sectors with respect to the total spin of the chain and the anisotropy. The conception of holes has to be changed in this case, because there occur more holes than expected. The finite-size corrections for the XXX model are calculated including complex roots and the new type of real solutions with repeating integers. The 'tower structure' predicted by the hypothesis of conformal invariance is shown to remain unchanged.Bethe ansatz equations (BAE) are investigated for the isotropic spin- 1 / 2 Heisenberg chain as well as the XXZ chain with real solutions characterized by identical integers in the logarithmic form of the BAE. Such states do not belong to the usual classification scheme (string hypothesis). They always exist in critical sectors with respect to the total spin of the chain and the anisotropy. The conception of holes has to be changed in this case, because there occur more holes than expected. The finite-size corrections for the XXX model are calculated including complex roots and the new type of real solutions with repeating integers. The 'tower structure' predicted by the hypothesis of conformal invariance is shown to remain unchanged.

Journal of Physics A Mathematical and GeneralJul 7, 199315 citations

Analysis of the Bethe ansatz equations of the XXZ model

O. Babelon, Hector J. de Vega, C.-M. Viallet

Nuclear Physics BMay 1, 1983137 citations

Classification of the string solutions of Bethe equations in an XXZ model of arbitrary spin

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