An efficient method of spin dynamics for long-range interacting systems

Ana María Rey

Kouki Fukui, Synge Todo

Zejian Li, Anna Delmonte, Xhek Turkeshi +1 more

Measurement-induced phases exhibit unconventional dynamics as emergent collective phenomena, yet their behavior in tailored interacting systems - crucial for quantum technologies - remains less understood. We develop a systematic toolbox to analyze monitored dynamics in long-range interacting systems, relevant to platforms like trapped ions and Rydberg atoms. Our method extends spin-wave theory to general dynamical generators at the quantum trajectory level, enabling access to a broader class of states than approaches based on density matrices. This allows efficient simulation of large-scale interacting spins and captures nonlinear dynamical features such as entanglement and trajectory correlations. We showcase the versatility of our framework by exploring entanglement phase transitions in a monitored spin system with power-law interactions in one and two dimensions, where the entanglement scaling changes from logarithm to volume law as the interaction range shortens, and by dwelling on how our method mitigates experimental post-selection challenges in detecting monitored quantum phases.

P. Bruno

Tatsuhiko Shirai, T. Mori

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.

Soyoung Jung, Manuel Berrondo