Long-range interacting quantum systems

TL;DR

This review explores the universal features and behaviors of quantum many-body systems with long-range interactions across various experimental platforms, highlighting recent research and the conditions for universality.

Contribution

It summarizes recent investigations into long-range interacting quantum systems, emphasizing universal features and regimes relevant for current experimental realizations.

Findings

Identification of universal scaling regimes in long-range quantum systems

Analysis of non-additive and extensive energy regimes

Comparison of long-range effects across different experimental platforms

Abstract

The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range, temperature, density and dimension can be changed. The existence of universal scaling regimes, where diverse physical systems and observables display quantitative agreement, generates a common framework, where the efforts of different research communities can be -- in some cases rigorously -- connected. Still, the application of this general framework to particular experimental realisations requires the identification of the regimes where the universality phenomenon is expected to appear. In the present review we summarise the recent investigations of many-body quantum systems with long-range interactions, which are currently realised in Rydberg atom arrays, dipolar systems, trapped ion setups and cold atoms in cavity experiments. Our main aim is to present and identify the common and (mostly) universal features induced by long-range interactions in the behaviour of quantum many-body systems. We will discuss both the case of very strong non-local couplings, i.e. the non-additive regime, and the one in which energy is extensive, but nevertheless low-energy, long wavelength properties are altered with respect to the short-range limit. Cases of competition with other local effects in the above mentioned setups are also reviewed.