Construction of Fractal Order and Phase Transition with Rydberg Atoms

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.

10 pages, 8 figures

References in corpus (12)

• Probing many-body dynamics on a 51-atom quantum simulator
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Local stabilizer codes in three dimensions without string logical operators
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Dynamical crystallization in a low-dimensional Rydberg gas
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Quantum phases of Rydberg atoms on a kagome lattice
• Single-Atom Addressing in Microtraps for Quantum-State Engineering using Rydberg Atoms
• Single-site Rydberg addressing in 3D atomic arrays for quantum computing with neutral atoms

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