# Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems

## TL;DR

This paper investigates heating rates in strongly interacting quantum lattice systems under periodic driving, revealing exponential regimes and connections to eigenstate thermalization, with implications for experimental probing.

## Contribution

It introduces a numerical linked cluster expansion approach to calculate heating rates and links these rates to the eigenstate thermalization hypothesis in both integrable and nonintegrable systems.

## Key findings

- Heating rates follow an exponential regime.
- Heating rates agree with Fermi's golden rule.
- Heating rates can be experimentally probed via drive frequency.

## Abstract

We study heating rates in strongly interacting quantum lattice systems in the thermodynamic limit. Using a numerical linked cluster expansion, we calculate the energy as a function of the driving time and find a robust exponential regime. The heating rates are shown to be in excellent agreement with Fermi's golden rule. We discuss the relationship between heating rates and, within the eigenstate thermalization hypothesis, the smooth function that characterizes the off-diagonal matrix elements of the drive operator in the eigenbasis of the static Hamiltonian. We show that such a function, in nonintegrable and (remarkably) integrable Hamiltonians, can be probed experimentally by studying heating rates as functions of the drive frequency.