The Roaming Bethe Roots: An Effective Bethe Ansatz Beyond Integrability

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 the effective Bethe ansatz degrades relatively quickly as the deformation parameter increases. The efficacy of the method thus offers a useful probe for characterizing the strength of integrability breaking. Within its regime of accuracy, it also provides a new representation of the eigenstates of nearly integrable models, enabling one to exploit the algebraic structure inherited from integrability.