Prethermalization has been extensively studied in systems close to
integrability. We discuss a more general, yet conceptually simpler, setup for
this phenomenon. We consider a--possibly nonintegrable--reference dynamics,
weakly perturbed so that the perturbation breaks at least one conservation
law. We argue then that the evolution of the system proceeds via intermediate
(generalized) equilibrium states of the reference dynamics. The motion on the
manifold of equilibrium states is governed by an autonomous equation, flowing
towards global equilibrium in a time of order 1/g^2, where g is the
perturbation strength. We also describe the leading correction to the time-
dependent reference equilibrium state, which is, in general, of order g [1].
The theory is well confirmed in numerical calculations of model Hamiltonians
in the context of quantum quenches [1] and driven systems [2], for which we
use numerical linked cluster expansions and full exact diagonalization. For
the driven systems, 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 [3], can be probed
experimentally by studying heating rates as functions of the frequency of the
drive.
References:
[1] K. Mallayya, MR, and W. De Roeck, Prethermalization and
Thermalization in Isolated Quantum Systems, Phys. Rev. X 9, 021027 (2019).
[2] K. Mallayya and MR, Heating Rates in Periodically Driven Strongly
Interacting Quantum Many-Body Systems, Phys. Rev. Lett. 123, 240603 (2019).
[3] T. LeBlond, K. Mallayya, L. Vidmar, and MR, Entanglement and matrix
elements of observables in interacting integrable systems, Phys. Rev. E 100,
062134 (2019).
Host: Jay Sau