Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermions and Quantum Spins

TL;DR

This paper investigates the quantum dynamics of lattice fermions and spins with long-range interactions, revealing complex classical-quantum entanglement and advancing the mathematical understanding of such systems.

Contribution

It introduces a new mathematical framework to analyze the quantum component of long-range interaction dynamics, surpassing previous studies.

Findings

Quantum dynamics involve intricate classical-quantum entanglement.

Long-range interactions lead to highly non-local quantum behavior.

New theoretical perspectives on macroscopic quantum systems.

Abstract

We study the macroscopic dynamics of fermion and quantum-spin systems with long-range, or mean-field, interactions, which turns out to be equivalent to an intricate combination of classical and short-range quantum dynamics. In this paper we focus on the \emph{quantum} part of the long-range macroscopic dynamics. The classical part is studied in a companion paper. Altogether, the results obtained are far beyond previous ones and required the development of a suitable mathematical framework. The entanglement of classical and quantum worlds is noteworthy, opening new theoretical perspectives, and is shown here to be a consequence of the highly non-local character of long-range, or mean-field, interactions.