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arXiv:2301.07127 · Physical Review Letters

Emergent Glassy Behavior in a Kagome Rydberg Atom Array

Yan Qing Zheng, Yan-Cheng Wang, Rhine Samajdar, Subir Sachdev A, Zi Yang Meng

Published May 18, 2023• 37 citations
arXivHTMLPDF

Abstract

We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.

DOI
10.1103/physrevlett.130.206501

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We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.
Abstract Rydberg atom array experiments have demonstrated the ability to act as powerful quantum simulators, preparing strongly-correlated phases of matter which are challenging to study for conventional computer simulations. A key direction has been the implementation of interactions on frustrated geometries, in an effort to prepare exotic many-body states such as spin liquids and glasses. In this paper, we apply two-dimensional recurrent neural network (RNN) wave functions to study the ground states of Rydberg atom arrays on the kagome lattice. We implement an annealing scheme to find the RNN variational parameters in regions of the phase diagram where exotic phases may occur, corresponding to rough optimization landscapes. For Rydberg atom array Hamiltonians studied previously on the kagome lattice, our RNN ground states show no evidence of exotic spin liquid or emergent glassy behavior. In the latter case, we argue that the presence of a non-zero Edwards-Anderson order parameter is an artifact of the long autocorrelations times experienced with quantum Monte Carlo (QMC) simulations, and we show that autocorrelations can be systematically reduced by increasing numerical effort. This result emphasizes the utility of autoregressive models, such as RNNs, in conjunction with QMC, to explore Rydberg atom array physics on frustrated lattices and beyond.
We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays.
A programmable quantum simulator using Rydberg-atom array provides a promising route to demystifying quantum many-body physics in strongly correlated systems. Motivated by the recent realization of various quantum magnetic phases on the frustrated Rydberg-atom array, we perform numerically exact quantum Monte Carlo simulations to investigate the exotic states of matter emerging in the model describing the Rydberg atom on a triangular lattice. Our state-of-the-art simulation unveils the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ triangular antiferromagnetic order exists at 1/31/31/3 or 2/32/32/3-Rydberg filling, consistent with the observation in experiments. Remarkably, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ long-range order arising from order-by-disorder mechanism emerges at 1/21/21/2 filling. At finite temperature, U(1)\mathrm{U}(1)U(1) symmetry is emergent at 1/21/21/2 filling and a Kosterlitz-Thouless phase transition occurs with increasing temperature. These intriguing phenomena are potentially detected in future Rydberg-atom experiments.
We consider the quench dynamics of a two-dimensional quantum dimer model and determine the role of its kinematic constraints. We interpret the nonequilibrium dynamics in terms of the underlying equilibrium phase transitions consisting of a Berezinskii-Kosterlitz-Thouless (BKT) transition between a columnar ordered valence bond solid (VBS) and a valence bond liquid (VBL), as well as a first-order transition between a staggered VBS and the VBL. We find that quenches from a columnar VBS are ergodic and both order parameters and spatial correlations quickly relax to their thermal equilibrium. By contrast, the staggered side of the first-order transition does not display thermalization on numerically accessible timescales. Based on the model's kinematic constraints, we uncover a mechanism of relaxation that rests on emergent, highly detuned multidefect processes in a staggered background, which gives rise to slow, glassy dynamics at low temperatures even in the thermodynamic limit.
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.
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.