Analytic Bethe Ansatz for 1-D Hubbard model and twisted coupled XY model

TL;DR

This paper derives eigenvalues for transfer matrices of the 1-D Hubbard and twisted coupled XY models using the analytic Bethe Ansatz, revealing their equivalence under certain conditions.

Contribution

It demonstrates the exact equivalence of the 1-D Hubbard model and the twisted coupled XY model at the Hamiltonian and transfer matrix levels.

Findings

Eigenvalues of transfer matrices derived for both models

Models share the same Bethe Ansatz equations under specific conditions

Proved the models are exactly equivalent under certain boundary conditions

Abstract

We found the eigenvalues of the transfer matrices for the 1-D Hubbard model and for the coupled XY model with twisted boundary condition by using the analytic Bethe Ansatz method. Under a particular condition the two models have the same Bethe Ansatz equations. We have also proved that the periodic 1-D Hubbard model is exactly equal to the coupled XY model with nontrivial twisted boundary condition at the level of hamiltonians and transfer matrices.