On Exponentially Long Prethermalization Timescales in Isolated Quantum Systems

Abstract

We study prethermalization in time-independent quantum many-body systems on a $d$-dimensional lattice with an extensive local Hamiltonian $H=N+\epsilon P$, in the regime where $\epsilon \ll 1$. We prove that the prethermal timescale is exponential in ${\epsilon }_0/\epsilon$, where ${\epsilon }_0$ is an explicit scale determined by the locality exponent and the local norm of $P$. We also construct two extensive local quasi-conserved quantities whose variation remains exponentially small throughout this time interval.

arXiv comment16 pages; corrected some misprints and added further explanation. Version accepted for publication on Studies in Applied Mathematics