Effective Bethe Ansatz for Spin-1 Non-integrable Models

Abstract

This work presents a comprehensive benchmark and validation of a recently proposed method called Effective Bethe Ansatz (EBA). It is a variational method that deforms the exact Bethe wavefunctions of one-dimensional spin chains at integrable points to approximate non-integrable systems. We apply this method to the non-integrable regime of the spin-1 bilinear-biquadratic chain. By performing EBA method starting from the two integrable endpoints, the Takhtajan-Babujian point and the Lai-Sutherland point, we systematically evaluate the accuracy of the EBA for the ground state and first excited state. Our validation is based on a direct comparison with exact diagonalization, assessing energy, fidelity, and entanglement entropy. The results confirm that the EBA provides a physically accurate description near integrability, with fidelity decreasing controllably as the perturbation increases. The method successfully captures key finite-size effects, such as level crossings, manifested as sharp drops in fidelity, and provides a probe to potential phase transitions. This study establishes the EBA as a reliable and efficient semi-analytical tool, clarifying its scope and limitations for studying low-energy physics in non-integrable quantum spin chains.

Figures (13)

• Figure 1: The parameter space of models we study in this work. At two ends $\beta=\pm 1$, there are two integrable models, and there is a special point $\beta=\frac{1}{3}$ at the middle, known as the AKLT model.
• Figure 2:
• Figure 3: Comparison between the entanglement entropy found by ED and EBA.
• Figure 4: Degeneracy of the ground state and the 1st excited state for spin chains of different $L$.
• Figure 5: Lowest energy levels found by EBA in each magnon sector in the $L=4$ spin chain at $\beta=0.8$.