The Bethe Ansatz and One-Dimensional Magnetic Systems.

Michael Fowler

After reviewing the basic ideas of the Bethe Ansatz using the simplest possible model—the one-dimensional interacting boson system of Leib and Liniger—we discuss the magnetic systems for which it has been used successfully. These include spin one-half chains, the Hubbard model, and the Kondo problem.

Marc Bellon, S. Boukraa, J.-M. Maillard +1 more

Y Wang, Fu‐Cho Pu

The one-dimensional (1D) electron gas model in the strong coupling regime is considered. It is shown that this model is Bethe ansatz solvable and the exact spectrum of the Hamiltonian is obtained. The massive spin elementary excitations are established based on the Bethe ansatz equations. The magnetization near the onset at zero temperature and the low-temperature thermodynamics are calculated.

L.V. Avdeev, Alexey A. Vladimirov

Yuanyuan Li, Junpeng Cao, Wen‐Li Yang +2 more

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.