Integrable construction of a two-dimensional lattice model with anisotropic Hubbard couplings
Ze Tao, Fujun Liu
TL;DR
The paper constructs a strictly solvable two-dimensional lattice with anisotropic Hubbard couplings by fusing a 2D, two-spin Yang–Baxter–compliant R-operator with a spin–charge interaction. It then solves the model via a nested algebraic Bethe ansatz to obtain exact transfer-matrix eigenvalues and two tiers of Bethe equations, and derives the explicit Hamiltonian through the logarithmic derivative at a regular point. The resulting $H^{(2D)}=H^{(x)}+H^{(y)}$ features anisotropic hopping, on-site $U$, and orbital coupling terms, reducing to the standard 1D Hubbard model in a 1D limit and to a free-fermion description as $U\to 0$. The genuine two-dimensional coupling is confirmed by $[H^{(x)},H^{(y)}]\neq 0$, and the work provides a new exactly solvable framework for exploring anisotropic strongly correlated systems with potential implications for condensed matter and holographic contexts.
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.