In this review recent investigations are summarized of many-body quantum systems with
long-range interactions, which are currently realized in Rydberg atom arrays, dipolar …

The study of critical properties of systems with long-range interactions has attracted, in
recent decades, a continuing interest and motivated the development of several analytical …

Several recent experiments in atomic, molecular, and optical systems motivated a huge
interest in the study of quantum long-range systems. Our goal in this paper is to present a …

Ensemble inequivalence, ie, the possibility of observing different thermodynamic properties
depending on the statistical ensemble which describes the system, is one of the hallmarks of …

Over the past few decades, tremendous efforts have been devoted to understanding self-
duality at the quantum critical point, which enlarges the global symmetry and constrains the …

A bstract In this paper we consider classical and quantum versions of the critical long-range
O (N) model, for which we study finite-size and finite-temperature effects, respectively, at …

The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a
topological phase transition without symmetry breaking, where a quasiordered phase …

Within the ultimate goal of classifying universality in quantum many-body dynamics,
understanding the relation between out-of-equilibrium and equilibrium criticality is a crucial …

Quantum long-range models at zero temperature can be described by fractional Lifshitz field
theories, that is, anisotropic models whose actions are short range in time and long range in …

Dimensional correspondences have a long history in critical phenomena. Here, we review
the effective dimension approach, which relates the scaling exponents of a critical system in …