Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions

TL;DR

This paper establishes bounds on energy absorption in long-range quantum systems under periodic driving, indicating the existence of prethermal regimes governed by effective Hamiltonians, supported by numerical evidence.

Contribution

It derives general bounds on energy absorption rates in long-range interacting quantum systems and demonstrates the exponential decay of absorption at high frequencies, implying prethermalization.

Findings

Energy absorption rate decays exponentially with frequency.

Prethermal plateau exists where dynamics are governed by an effective Hamiltonian.

Numerical evidence supports the theoretical bounds and prethermalization.

Abstract

Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as $1/r^\alpha$ with $\alpha > d/2$. We show that the disordered averaged energy absorption rate at high temperature decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of both heating and hence new dynamical regimes described by effective Hamiltonians in such long-range systems.