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

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.

11 pages, 4 figures. Invited contribution to the STATPHYS26 Special Issue in JSTAT