Integrable construction of a two-dimensional lattice model with anisotropic Hubbard couplings

TL;DR

This paper constructs an exactly solvable two-dimensional lattice model with anisotropic Hubbard interactions using integrability techniques, providing explicit eigenvalues and a local Hamiltonian.

Contribution

It introduces a new integrable 2D lattice model with anisotropic Hubbard couplings, derived from a graded R-operator satisfying the Yang-Baxter equation.

Findings

Exact eigenvalues of the transfer matrix obtained

Bethe equations derived for the model

Explicit local Hamiltonian with anisotropic interactions

Abstract

By defining a graded global R-operator $\mathbb{R}_{ab}^{(2D,2S)}$ that couples free-fermion structures and incorporates anisotropic Hubbard interactions while satisfying the Yang--Baxter equation, we construct a strictly solvable two-dimensional lattice model. We then build the layer-to-layer transfer matrix through a bidirectional-monodromy construction and prove the model's integrability via the associated global RTT relations. Using the nested algebraic Bethe ansatz, we obtain the exact eigenvalues of the transfer matrix and derive the corresponding first- and second-level Bethe equations. Finally, by taking the logarithmic derivative of the transfer matrix at the regular point, we recover explicitly a local Hamiltonian that features anisotropic hopping, an on-site Hubbard interaction, and orbital-coupling contributions.