$N$-Scaling of Timescales in Long-Range $N$-Body Quantum Systems

TL;DR

This paper surveys how relaxation times in long-range quantum spin systems scale with particle number, highlighting their rapid equilibration and implications for understanding quantum thermalization.

Contribution

It provides a comprehensive overview of the N-scaling of relaxation times in long-range quantum systems and suggests the universality of this behavior using Lieb-Robinson bounds.

Findings

Relaxation times scale with system size N.

Long-range interactions lead to rapid equilibration.

Lieb-Robinson bounds support the universality of scaling.

Abstract

Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on long-range quantum spin models that illustrate this scaling behaviour, and provide indications for its common occurrence by making use of Lieb-Robinson bounds. I argue that these findings may help in understanding the extraordinarily short equilibration timescales predicted by typicality techniques.