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

K. Isler, Manu B. Paranjape

Anatol N. Kirillov, Nicolai Reshetikhin

K. Isler, Manu B. Paranjape

Yoichi Kazama, Shota Komatsu, Takuya Nishimura

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.

Fabian H. L. Eßler, V. E. Korepin, Kareljan Schoutens

The authors analyse the Bethe ansatz equations for the two-particle sector of the spin 1/2 Heisenberg XXX model on a one-dimensional lattice of length N. They show that, beginning at a critical lattice length of N=21.86, new pairs of real solutions develop, whereas complex solutions start to disappear. The integers (that appear in the logarithmic form of the Bethe equations) of the new solutions do not fit into the conventional classification scheme. The total number of solutions in the two-particle sector remains unchanged and is in agreement with the claim that the SU(2) extended Bethe ansatz gives a complete set of 2 N eigenstates.