# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1706.07207