Construction of Fractal Order and Phase Transition with Rydberg Atoms

TL;DR

This paper proposes creating a fractal-structured many-body phase using Rydberg atoms, demonstrating the potential for simulating exotic fractal phases and phase transitions in quantum systems.

Contribution

It introduces a method to realize fractal order and phase transitions with Rydberg atom arrays, overcoming multi-spin interaction challenges in condensed matter platforms.

Findings

Demonstrates the simulation of fractal structures with Rydberg atoms

Shows the possibility of studying fractal phase transitions

Highlights the tunability of Rydberg platforms for exotic phases

Abstract

We propose the construction of a many-body phase of matter with fractal structure using arrays of Rydberg atoms. The degenerate low energy excited states of this phase form a self-similar fractal structure. This phase is analogous to the so-called "type-II fracton topological states". The main challenge in realizing fracton-like models in standard condensed matter platforms is the creation of multi-spin interactions, since realistic systems are typically dominated by two-body interactions. In this work, we demonstrate that the Van der Waals interaction and experimental tunability of Rydberg-based platforms enable the simulation of exotic phases of matter with fractal structures, and the study of a quantum phase transition involving a fractal ordered phase.