Thermalization timescales in quantum systems with super-long-range interactions

Advances in atomic and molecular platforms have enabled the realization of long-range interacting quantum systems with power law decaying interactions. While these systems display rich nonequilibrium dynamics, the timescales governing their approach to thermal equilibrium remain poorly understood. We address this issue by analyzing spin chains with long-range interactions and uncovering how interaction range controls relaxation and prethermalization timescales. Starting from spin models in the all-to-all coupling limit, we show that even an infinitesimal power-law ex- ponent is sufficient to induce quantum chaos [1], thereby enforcing the eigenstate thermalization hypothesis (ETH). However, the validity of ETH alone does not explain the hierarchy of dynamical timescales. We demonstrate that for the power-law exponent near zero, weak integrability breaking gives rise to emer- gent quasi-conserved quantities, producing long-lived prethermal plateaus. Despite compliance with ETH, the approach to true thermal equilibrium in these systems can be exceedingly slow.

[1] Soumya Kanti Pal and Lea F Santos. Fragmented eigenstate thermalization versus robust integrability in long-range models, 2025. arXiv:2508.00077.