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arXiv:2506.11985 · Physical Review Letters

Infinite Randomness Criticality and Localization of the Floating Phase in Arrays of Rydberg Atoms Trapped with Nonperfect Tweezers

Jose Soto Garcia, Natalia Chepiga

Published Jan 6, 2026• 2 citations
arXivHTMLPDF

Abstract

Chains of Rydberg atoms have emerged as a powerful platform for exploring low-dimensional quantum physics. This success originates from the precise control of lattice geometries provided by optical tweezers, which allows access to a wide range of synthetic quantum phases. Experiments on one-dimensional arrays have stimulated tremendous progress in understanding quantum phase transitions into crystalline phases. However, the finite width of tweezers introduces small variations in interatomic distances, leading to quenched disorder in the interactions. In this Letter, we numerically study how such disorder alters the nature of two critical regimes observed in experiments. First, following experimental protocols, we analyze Kibble-Zurek dynamics and find a crossover from the clean Ising transition to the infinite-randomness fixed point as system size and disorder strength increase. Second, we show that the floating phase-an incommensurate Luttinger liquid phase emerging at stronger interactions-is localized by the disorder, yet preserves short-range incommensurate correlations with the same leading wave vector. Our results clearly reveal an additional conceptual challenge in understanding critical phenomena using Rydberg-based quantum simulators.

DOI
10.1103/tmyk-b1yv

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Chains of Rydberg atoms have emerged as a powerful platform for exploring low-dimensional quantum physics. This success originates from the precise control of lattice geometries provided by optical tweezers, which allows access to a wide range of synthetic quantum phases. Experiments on one-dimensional arrays have stimulated tremendous progress in understanding quantum phase transitions into crystalline phases. However, the finite width of tweezers introduces small variations in interatomic distances, leading to quenched disorder in the interactions. In this Letter, we numerically study how such disorder alters the nature of two critical regimes observed in experiments. First, following experimental protocols, we analyze Kibble-Zurek dynamics and find a crossover from the clean Ising transition to the infinite-randomness fixed point as system size and disorder strength increase. Second, we show that the floating phase-an incommensurate Luttinger liquid phase emerging at stronger interactions-is localized by the disorder, yet preserves short-range incommensurate correlations with the same leading wave vector. Our results clearly reveal an additional conceptual challenge in understanding critical phenomena using Rydberg-based quantum simulators.
The floating phase, a critical incommensurate phase, has been theoretically predicted as a potential intermediate phase between crystalline ordered and disordered phases. In this study, we investigate the different quantum phases that arise in ladder arrays comprising up to 92 neutral-atom qubits and experimentally observe the emergence of the quantum floating phase. We analyze the site-resolved Rydberg state densities and the distribution of state occurrences. The site-resolved measurement reveals the formation of domain walls within the commensurate ordered phase, which subsequently proliferate and give rise to the floating phase with incommensurate quasi-long-range order. By analyzing the Fourier spectra of the Rydberg density-density correlations, we observe clear signatures of the incommensurate wave order of the floating phase. Furthermore, as the experimental system sizes increase, we show that the wave vectors approach a continuum of values incommensurate with the lattice. Our work motivates future studies to further explore the nature of commensurate-incommensurate phase transitions and their non-equilibrium physics. The critical floating phase can bridge crystalline orders and the disordered phase. Here, the authors experimentally observe the quantum floating phase in neutral atom qubit arrays, revealing domain walls and incommensurate quasi long-range order, and analyse its emergence via Fourier spectroscopy.
Rydberg atom arrays promise high-fidelity quantum simulations of critical phenomena with flexible geometries. Yet, experimental realizations inevitably suffer from disorder due to random displacements of atoms, leading to departures from the expected behavior. Here, we study how such positional disorder influences the Ising criticality. Since disorder breaks the Z2{\mathbb{Z}}_{2}Z2​ symmetry, one might expect the system to flow to an infinite-strength disordered fixed point, erasing all nontrivial critical features in low spatial dimensions. Remarkably, we find instead that disorder in Rydberg systems is subjected to nontrivial local constraints, making the physics markedly different from systems with more conventional spatially short-range correlated or long-range correlated disorder. This leads to new classes of criticalities even at dimensions where conventional disorder would destroy criticality altogether. We then demonstrate as a consequence how a pseudocriticality emerges in Rydberg atom chains of experimentally realistic scale, and show that the renormalization group flow is governed by a locally constrained Z2{\mathbb{Z}}_{2}Z2​-breaking perturbation. Our findings uncover disorder-driven phenomena and underscore the importance of carefully treating disorder effects in quantum simulators.
We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, ${V}_{ij}\ensuremath{\propto}{\left|i\ensuremath{-}j\right|}^{\ensuremath{-}\ensuremath{\alpha}}$, where the exponent of the interaction range $\ensuremath{\alpha}$ can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing $\ensuremath{\alpha}$, the critical exponent experiences a sharp increase at about ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}1.2$ and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$, we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$, the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.
Dual-species Rydberg atom arrays extend single-species platforms by introducing competing interaction scales and enhanced quantum fluctuations, enabling phenomena beyond homogeneous settings. In this work, we study the ground-state phase diagram of a one-dimensional dual-species Rydberg atom ladder using large-scale density-matrix renormalization group calculations. We identify disordered phases, multiple ordered phases with Z2\mathbb{Z}_2Z2​, Z3\mathbb{Z}_3Z3​, and Z4\mathbb{Z}_4Z4​ symmetry, as well as floating phases characterized by incommensurate wave vectors and algebraically decaying correlations. Importantly, we observe a smooth crossover between distinct Z2\mathbb{Z}_2Z2​-ordered regimes, reflecting a reorganization of low-energy degrees of freedom rather than a true phase transition, which is absent in single-species Rydberg arrays. We further uncover a multi-critical point at the boundary between the Z2⊗Z2\mathbb{Z}_2 \otimes \mathbb{Z}_2Z2​⊗Z2​ and Z3⊗Z3\mathbb{Z}_3 \otimes \mathbb{Z}_3Z3​⊗Z3​ ordered phases, where Ising, chiral, and first-order transition lines intersect. Our results demonstrate that dual-species Rydberg atom arrays provide a unique platform for realizing crossover physics and multi-critical behavior inaccessible in single-species architectures.
We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.
The Kibble-Zurek scaling reveals the universal dynamics when a system is linearly ramped across a symmetry-breaking phase transition. However, in reality, inevitable finite-size effects or symmetry-breaking perturbations can often smear out the critical point and render the phase transition into a smooth crossover. In this Letter, we show experimentally that the precise Kibble-Zurek scaling can be retained in the near-critical crossover regime, not necessarily crossing the critical point strictly. The key ingredient to achieving this near-critical Kibble-Zurek scaling is that the system size and the symmetry-breaking field must be appropriately scaled following the variation of ramping speeds. The experiment is performed in a reconfigurable Rydberg atom array platform, where the Rydberg blockade effect induces a Z_{2} symmetry-breaking transition. The atom array platform enables precise control of the system size and the zigzag geometry as a symmetry-breaking field. Therefore, we can demonstrate notable differences in the precision of the Kibble-Zurek scaling with or without properly scaling the system size and the zigzag geometry. Our results strengthen the Kibble-Zurek scaling as an increasingly valuable tool for investigating phase transition in quantum simulation platforms.