Bethe ansatz solvable interacting particle systems on Z

Tomohiro SASAMOTO

Franz G. Mertens, Manfred Hader

Ladislav Šamaj, Zoltán Bajnok

Hans-Peter Eckle

Abstract The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ansatz. Electronic systems are the most relevant examples for condensed matter physics. Prominent electronic many-particle systems in one dimension solvable by a nested Bethe ansatz are the one-dimensional δ-Fermi gas, the one-dimensional Hubbard model, and the Kondo model. The major difference to the Bethe ansatz for one component systems is a second, spin, eigenvalue problem, which has the same form in all cases and is solvable by a second Bethe ansatz, e.g. an algebraic Bethe ansatz. A quantum dot tuned to Kondo resonance and coupled to an isolated metallic ring presents an application of the coupled sets of Bethe ansatz equations of the nested Bethe ansatz.

Jens Bolte, George Garforth

We introduce n-particle quantum graphs with singular two-particle interactions in such a way that eigenfunctions can be given in the form of a Bethe ansatz. We show that this leads to a secular equation characterising eigenvalues of the Hamiltonian that is based on a finite-dimensional determinant. These findings generalise previous results about two-particle quantum graphs.

Yupeng Wang, Wen‐Li Yang, Junpeng Cao +1 more