On Exponentially Long Prethermalization Timescales in Isolated Quantum Systems

TL;DR

This paper demonstrates that in certain quantum many-body systems, prethermalization can last exponentially long due to quasi-conserved quantities, with implications for understanding thermalization timescales.

Contribution

It establishes that prethermalization timescales are exponentially large in the inverse of a small perturbation parameter, revealing new insights into quantum dynamics.

Findings

Prethermalization time is exponentially large in the ratio 544/44.

Existence of two quasi-conserved quantities for exponentially long times.

Prethermalization persists with exponentially small errors in the regime studied.

Abstract

We study prethermalization in time-independent quantum many-body systems on a $d$-dimensional lattice with an extensive local Hamiltonian $H=N+\varepsilon P$, in the regime where $\varepsilon \ll 1$. We show that the prethermalization time is exponentially large in $\varepsilon_0/\varepsilon$, where $\varepsilon_0$ is the ratio between an effective spectral gap width and the local norm of $P$. We prove also that for exponentially long times, there exist two quasi-conserved quantities up to exponentially small errors.