  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.
