Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions

TL;DR

This paper analyzes the $D_2^{(2)}$ quantum spin chain with open boundaries, deriving Bethe ansatz equations and calculating surface and excitation energies analytically for various boundary conditions.

Contribution

It provides the first analytical derivation of Bethe ansatz equations and energy spectra for the $D_2^{(2)}$ model with generic open boundaries, using the $t$-$W$ method.

Findings

Derived homogeneous Bethe ansatz equations for the model.

Computed surface energies analytically.

Determined excitation energies in different boundary regimes.

Abstract

We study the quantum integrable spin chain model associated with the twisted $D_2^{(2)}$ algebra (or simply the $D_2^{(2)}$ model) under generic open boundary conditions. The Hamiltonian of this model can be factorized into the sum of two staggered XXZ spin chains. Applying the $t$-$W$ method, we derive the homogeneous Bethe ansatz equations for the zeros of the transfer matrix eigenvalues and the patterns of the corresponding zeros of the staggered XXZ spin chain with generic integrable boundaries. Based on these results, we analytically compute the surface energies and excitation energies of the $D_2^{(2)}$ model in different regimes of boundary parameters.