Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions

TL;DR

This paper reviews recent theoretical advances in the out-of-equilibrium dynamics of long-range interacting quantum many-body systems, highlighting novel phenomena and unifying frameworks bridging mean-field and many-body physics.

Contribution

It introduces a versatile formalism that interpolates between few-body mean-field and many-body quasi-local regimes, connecting different interaction scales in long-range quantum systems.

Findings

Non-ballistic quantum correlation spreading

Slowdown of entanglement dynamics

Suppression of thermalization and equilibration

Abstract

Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of these systems enables novel non-equilibrium phenomena with no counterpart in conventional quantum systems with local interactions. Much of the theory work in this area either focussed on the impact of variable-range interaction tails on the physics of local interactions or relied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recent advances in the field. Working with prototypical interacting quantum spin lattices without disorder, our presentation hinges upon a versatile theoretical formalism that interpolates between the few-body mean-field physics and the many-body physics of quasi-local interactions. Such a formalism allows us to connect these two regimes, providing both a formal quantitative tool and basic physical intuition. We leverage this unifying framework to review several findings of the last decade, including the peculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdown of entanglement dynamics, suppression of thermalization and equilibration, anomalous scaling of defects upon traversing criticality, dynamical phase transitions, and genuinely non-equilibrium phases stabilized by periodic driving. The style of this Report is on the pedagogical side, which makes it accessible to readers without previous experience in the subject matter.