From few- to many-body quantum systems

TL;DR

This paper investigates how many particles are needed for a quantum system to exhibit many-body characteristics, finding that static properties converge quickly while dynamics depend on initial states and evolve differently.

Contribution

The study provides a systematic comparison of few-particle systems with the many-body limit, highlighting the rapid convergence of static properties and the conditions under which many-body chaos signatures emerge.

Findings

Static properties converge rapidly for N ≥ 4

Density of states approaches Gaussian form

Signatures of quantum chaos become evident

Abstract

How many particles are necessary to make a quantum system many-body? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with $N$ particles, gradually increasing $N$ from 1. We show that convergence for the static properties of the system with few particles to the many-body limit is fast. For $N \gsim 4$, the density of states is already very close to Gaussian and signatures of many-body quantum chaos, such as level repulsion and fully extended eigenstates, become evident. The dynamics, on the other hand, depend on the initial state and time scale. In dilute systems, as the particles move away from each other, the entropy growth changes in time from linear, as typical for many-body systems, to logarithmic.