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arXiv:2108.07765 · Physical Review Letters

Construction of Fractal Order and Phase Transition with Rydberg Atoms

Nayan E. Myerson-Jain, Stephen Yan, David Weld, Cenke Xu

Published Jan 5, 2022• 34 citations
arXivHTMLPDF

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 fractonlike models in standard condensed matter platforms is the creation of multispin 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.

DOI
10.1103/physrevlett.128.017601

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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 fractonlike models in standard condensed matter platforms is the creation of multispin 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.
We describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.
Competing short- and long-range interactions represent distinguished ingredients for the formation of complex quantum many-body phases. Their study is hard to realize with conventional quantum simulators. In this regard, Rydberg atoms provide an exception as their excited manifold of states have both density-density and exchange interactions whose strength and range can vary considerably. Focusing on one-dimensional systems, we leverage the Van der Waals and dipole-dipole interactions of the Rydberg atoms to obtain the zero-temperature phase diagram for a uniform chain and a dimer model. For the uniform chain, we can influence the boundaries between ordered phases and a Luttinger liquid phase. For the dimerized case, a new type of bond-order-density-wave phase is identified. This demonstrates the versatility of the Rydberg platform in studying physics involving short- and long-ranged interactions simultaneously.
Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z_{2} gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological Z_{2} quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also discuss the natures of the fractionalized excitations of these Z_{2} spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.
Rydberg atoms trapped by optical tweezers have emerged as a versatile platform to emulate lattices with different geometries, in which long-range interacting spins lead to fascinating phenomena, ranging from spin liquids to topological states of matter. Here, we show that when the lattice has a fractal geometry with Hausdorff dimension 1.58, additional surprises appear. The system is described by a transverse-field Ising model with long-range van der Waals interactions in a Sierpinski gasket fractal. We investigate the problem theoretically using exact diagonalization, variational mean field, quantum Monte Carlo, and a graph-based numerical technique, SIM-GRAPH, which we developed. We find that in the quantum regime, the phase diagram exhibits phases in which the spins flip one-by-one. The theoretical results are in excellent agreement with experiments performed with single 88Sr atoms trapped by optical tweezers arranged in a fractal geometry. The magnetization and von Neumann entanglement entropy reveal several regimes in which single spin-flips are delocalized over many sites of one sublattice, thus allowing for an unprecedented control of a cascade of phase transitions in a manybody system. These results expand the possibilities of Rydberg atoms for quantum information processing and may have profound implications in quantum technology.
Programmable arrays of neutral Rydberg atoms are one of the leading platforms today for scalable quantum simulation and computation. In these systems, the dipole-dipole interactions between the individual atoms, or qubits, typically result in binary -- i.e., two-body -- couplings. In this work, we develop an experimentally accessible scheme for engineering three-body interactions in Rydberg lattices. Such strong three-body couplings can fundamentally modify the underlying physics compared to systems with only two-body interactions: we demonstrate this, in particular, by systematically investigating the effective many-body Hamiltonian and its emergent quantum phases. This capability paves the way for the quantum simulation of a broader class of correlated models of condensed matter and high-energy physics.
Rydberg atom arrays have recently emerged to be a promising platform for the exploration of exotic quantum phases of matter and quantum phenomena. In this work, we map out the ground-state phase diagram of Rydberg atoms on a honeycomb lattice as a function of the Rydberg blockade radius and the laser detuning by performing large-scale finite-size density matrix renormalization group simulations. Apart from a featureless disordered phase, we find five other intricate long-range density-wave-ordered phases within a relatively wide parameter space. The properties of these quantum phases are analyzed by calculating their Rydberg excitation profiles and static structure factors. In addition, a continuous quantum phase transition belonging to the (2+1)-dimensional Ising universality class is explored by a standard finite-size scaling analysis. Our work implies some different physics, such as the possible nontrivial quantum phase transitions and a highly degenerate string ordered phase, that a honeycomb geometry could bring to the Rydberg system and serves as a numerical guide for possible real experiments.