The Roaming Bethe Roots: An Effective Bethe Ansatz Beyond Integrability
Wenlong Zhao, Yunfeng Jiang, Rui-Dong Zhu

TL;DR
The paper introduces an effective Bethe ansatz method that approximates eigenstates of nearly integrable quantum many-body systems by renormalizing Bethe roots, providing high accuracy for weak integrability-breaking.
Contribution
It develops a novel approach to extend Bethe ansatz techniques beyond integrability by optimizing Bethe roots to approximate non-integrable models.
Findings
High-quality approximation for weak integrability-breaking
Degradation of accuracy with strong integrability-breaking
Provides a new representation of eigenstates in nearly integrable models
Abstract
We propose an effective Bethe ansatz for solving quantum many-body systems near an integrable point. Our approach retains the functional form of the Bethe wave function while renormalizing the Bethe roots to account for integrability-breaking interactions. These effective roots are determined by minimizing physically motivated cost functions. The resulting off-shell Bethe states serve as approximate eigenstates of the non-integrable models. We assess the quality of the approximation using various physical observables, including the energy eigenvalue, state fidelity, and bipartite entanglement entropy. Our tests show that for models with weak integrability-breaking, the effective Bethe ansatz provides a high-quality approximation to the exact eigenstates over a wide range of deformation parameters. In contrast, for models with strong integrability-breaking interactions, the efficacy of…
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