Quantum Chaos in the Heisenberg Spin Chain: the Effect of Dzyaloshinskii-Moriya Interaction

TL;DR

This paper investigates how Dzyaloshinskii-Moriya interaction influences the emergence of quantum chaos in various integrable spin-1/2 chains, revealing model-dependent effects and implications for thermalization.

Contribution

It demonstrates that Dzyaloshinskii-Moriya interaction induces quantum chaos in Ising and XXZ models but not in the XX model, clarifying its role in quantum many-body systems.

Findings

Quantum chaos appears in Ising and XXZ models with Dzyaloshinskii-Moriya interaction.

No evidence of chaos in the XX model after adding the interaction.

Discusses the link between quantum chaos and thermalization.

Abstract

Using one-dimensional spin-1/2 systems as prototypes of quantum many-body systems, we study the emergence of quantum chaos. The main purpose of this work is to answer the following question: how does the spin-orbit interaction, as a pure quantum interaction, may lead to the onset of quantum chaos? We consider three integrable spin-1/2 systems: the Ising, the XX, and the XXZ limits, and analyze whether quantum chaos develops or not after the addition of the Dzyaloshinskii-Moriya interaction. We find that, depending on the strength of the anisotropy parameter, the answer is positive for the XXZ and Ising models, while no such evidence is observed for the XX model. We also discuss the relationship between quantum chaos and thermalization.