Integrable Chain Model with Additional Staggered Model Parameter

TL;DR

This paper generalizes the Yang-Baxter equations to include Z_2 grading, constructs an integrable staggered XXZ model with complex interactions, and solves it using the Algebraic Bethe Ansatz, revealing new boundary conditions and limits.

Contribution

It introduces a generalized integrable model with staggered parameters and solves it explicitly, expanding the class of known integrable systems.

Findings

The model includes three-site interactions resembling a zig-zag ladder.

Eigenstates and eigenvalues are obtained via Algebraic Bethe Ansatz.

The model exhibits a free fermionic limit at Δ=0 with boundary terms.

Abstract

The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented. The XXZ model with staggered disposition along a chain of both, the anisotropy \pm\Delta, as well as shifts of the spectral parameters are considered and the corresponding integrable model is constructed. The Hamiltonian of the model is computed in fermionic and spin formulations. It involves three neighbour site interactions and therefore can be considered as a zig-zag ladder model. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found. The model has a free fermionic limit at \Delta=0 and the integrable boundary terms are found in this case. This construction is quite general and can be applied to other known integrable models.