Geometry-driven transitions in sparse long-range spin models with cold atoms

TL;DR

This paper investigates how the geometry of sparse long-range spin models influences their critical behavior, revealing that structural changes in the interaction graph drive phase transitions and can be engineered in cold atom experiments.

Contribution

It introduces a geometry-driven framework for understanding phase transitions in long-range spin models, linking graph structure changes to critical phenomena and experimental realizations.

Findings

Geometry controls criticality and phase boundaries.

Structural changes in the interaction graph coincide with phase transitions.

Framework applicable to cold atom experiments with Rydberg atoms.

Abstract

We explore the influence of geometry in the critical behavior of sparse long-range spin models. We examine a model with interactions that can be continuously tuned to induce distinct changes in the metric, topology, and dimensionality of the coupling graph. This underlying geometry acts as the driver of criticality, with structural changes in the graph coinciding with and dictating the phase boundaries. We further discuss how this framework connects naturally to realizations in tweezer arrays with Rydberg excitations. In certain cases, the effective geometry can be incorporated in the layout of atoms in tweezers to realize phase transitions that preserve universal features, simplifying their implementation in near-term experiments.