Out-of-time-order correlator computation based on discrete truncated Wigner approximation

TL;DR

This paper introduces a discrete truncated Wigner approximation method to compute out-of-time-order correlators, effectively capturing quantum information scrambling in long-range interacting spin systems across various regimes.

Contribution

The paper presents a novel DTWA-based approach for simulating out-of-time-order correlators in long-range quantum spin systems, highlighting its accuracy and limitations.

Findings

DTWA accurately reproduces exact dynamics in strongly long-range systems.

Limitations of DTWA in weakly long-range systems and fast scrambling regimes.

Scrambling time scaling varies with interaction range and system size.

Abstract

We propose a method based on the discrete truncated Wigner approximation (DTWA) for computing out-of-time-order correlators. This method is applied to long-range interacting quantum spin systems where the interactions decay as a power law with distance. As a demonstration, we use a squared commutator of local operators and its higher-order extensions that describe quantum information scrambling under Hamilton dynamics. Our results reveal that the DTWA method accurately reproduces the exact dynamics of the average spreading of quantum information (i.e., the squared commutator) across all time regimes in strongly long-range interacting systems. We also identify limitations in the DTWA method when capturing dynamics in weakly long-range interacting systems and the fastest spreading of quantum information. Then we apply the DTWA method to investigate the system-size dependence of the scrambling time in strongly long-range interacting systems. We reveal that the scaling behavior of the scrambling time for large system sizes qualitatively changes depending on the interaction range. This work provides and demonstrates a new technique to study scrambling dynamics in long-range interacting quantum spin systems.