# Locality and Heating in Periodically Driven, Power-law Interacting Systems

## TL;DR

This paper investigates the heating times in periodically driven power-law interacting systems, demonstrating exponential long heating times under certain conditions and extending Lieb-Robinson bounds to higher-order interactions.

## Contribution

It introduces generalized bounds for power-law systems, extends analysis beyond linear response, and explores the implications of Lieb-Robinson bounds on heating times.

## Key findings

- Heating time is exponentially long for lpha > D under linear response.
- Existence of quasi-conserved observables for lpha > 2D.
- Extended Lieb-Robinson bounds for k-body interactions.

## Abstract

We study the heating time in periodically driven $D$-dimensional systems with interactions that decay with the distance $r$ as a power-law $1/r^\alpha$. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for $\alpha>D$. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for $\alpha>2D$. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to $k$-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.