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.

arXiv comment10 pages, 8 figures

References in corpus (48)

• Fault-tolerant quantum computation by anyons
• Quantum information with Rydberg atoms
• Nonequilibrium dynamics of closed interacting quantum systems
• 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
• Zoo of quantum-topological phases of matter
• 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
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Quantum Glassiness
• Fractons
• ARC: An open-source library for calculating properties of alkali Rydberg atoms
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Fracton Phases of Matter
• Site-resolved measurement of the spin-correlation function in the Hubbard model
• Realization of an anomalous Floquet topological system with ultracold atoms
• Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators
• Dynamical crystallization in a low-dimensional Rydberg gas
• Exotic topological order in fractal spin liquids
• Design and characterization of electronic fractals
• Topological order in an exactly solvable 3D spin model
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Quantum phases of Rydberg atoms on a kagome lattice
• Glassy quantum dynamics in translation invariant fracton models
• Measuring topology by dynamics: Chern number from linking number
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Floquet symmetry-protected topological phases in cold atomic systems
• Glassy dynamics and aging in an exactly solvable spin model
• Dynamical scar states in driven fracton systems
• Strong-weak coupling self-duality in the two-dimensional quantum phase transition of $p+ip$ superconducting arrays
• Fractal Symmetric Phases of Matter
• Single-Atom Addressing in Microtraps for Quantum-State Engineering using Rydberg Atoms
• Bond algebraic liquid phase in strongly correlated multiflavor cold atom systems
• Localization from superselection rules in translation invariant systems
• Glassiness through the emergence of effective dynamical constraints in interacting systems
• Fractionalization in Superconductor Josephson Junction Arrays Hinged by Quantum Spin Hall edges
• Quantifying and controlling prethermal nonergodicity in interacting Floquet matter
• Fractons from polarons
• Quantum quench and non-equilibrium dynamics in lattice-confined spinor condensates
• Majorana Quantum Lego, a Route Towards Fracton Matter
• Trajectory phase transitions in non-interacting spin systems
• Single-site Rydberg addressing in 3D atomic arrays for quantum computing with neutral atoms
• Electric Circuit Realizations of Fracton Physics

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• Exponential $U(1)$ Symmetry-Breaking Phase as a Disorder-Free Quantum Glass