Predicting the dynamical properties of topological matter is a challenging task, not only in theoretical and experimental settings, but also computationally. Numerical studies are often constrained to studying simplified models and lattices. Here we propose a time-dependent correlated ansatz for the dynamical preparation of a quantum-spin-liquid state on a Rydberg atom simulator. Together with a time-dependent variational Monte Carlo technique, we can faithfully represent the state of the system throughout the entire dynamical preparation protocol. We are able to match not only the physically correct form of the Rydberg atom Hamiltonian but also the relevant lattice topology at system sizes that exceed current experimental capabilities. This approach gives access to global quantities such as the topological entanglement entropy, providing insight into the topological properties of the system. Our results confirm the topological properties of the state during the dynamical preparation protocol, and deepen our understanding of topological entanglement dynamics. We show that, while the simulated state exhibits local properties resembling those of a resonating-valence-bond state, in agreement with experimental observations, it lacks the latter's characteristic topological entanglement entropy signature irrespective of the degree of adiabaticity of the protocol.
Predicting the dynamical properties of topological matter is a challenging task, not only in theoretical and experimental settings, but also computationally. Numerical studies are often constrained to studying simplified models and lattices. Here we propose a time-dependent correlated ansatz for the dynamical preparation of a quantum-spin-liquid state on a Rydberg atom simulator. Together with a time-dependent variational Monte Carlo technique, we can faithfully represent the state of the system throughout the entire dynamical preparation protocol. We are able to match not only the physically correct form of the Rydberg atom Hamiltonian but also the relevant lattice topology at system sizes that exceed current experimental capabilities. This approach gives access to global quantities such as the topological entanglement entropy, providing insight into the topological properties of the system. Our results confirm the topological properties of the state during the dynamical preparation protocol, and deepen our understanding of topological entanglement dynamics. We show that, while the simulated state exhibits local properties resembling those of a resonating-valence-bond state, in agreement with experimental observations, it lacks the latter's characteristic topological entanglement entropy signature irrespective of the degree of adiabaticity of the protocol.
Quantum spin liquids are elusive long-range entangled states. Motivated by experiments in Rydberg quantum simulators, recent excitement has centered on the possibility of dynamically preparing a state with quantum spin liquid correlation even when the ground state phase diagram does not exhibit such a topological phase. Understanding the microscopic nature of such quantum spin "lake" states and their relationship to equilibrium spin liquid order remains an essential question. Here, we extend the use of approximately symmetric neural quantum states for real-time evolution and directly simulate the dynamical preparation in systems of up to N=384 atoms. We analyze a variety of spin liquid diagnostics as a function of the preparation protocol and optimize the extent of the quantum spin lake thus obtained. In the optimal case, the prepared state shows spin-liquid properties extending over half the system size, with a topological entanglement entropy plateauing close to γ=ln2. We extract two physical length scales λ and ξ which constrain the extent of the quantum spin lake ℓ from above and below.
We experimentally investigate a frustrated spin-exchange antiferromagnet in a quantum simulator, composed of N = 114 dipolar Rydberg atoms arranged into a kagome array. Motivated by a recent theoretical proposal of a gapless U(1) Dirac spin liquid ground state, we use local addressing to adiabatically prepare low-energy states. We measure the local polarization and spin-spin correlations over this adiabatic protocol, and observe our system move from a staggered product state, through an intermediate magnetic crystal, and finally into a disordered, correlated liquid. We estimate the entropy density of this atomic liquid to be similar to that of frustrated magnetic insulators at liquid nitrogen temperatures. We compare the correlations in our liquid to those of a simple, parameter-free ansatz for the Dirac spin liquid, and find good agreement in the sign structure and spatial decay. Finally, we probe the static susceptibility of our system to a local field perturbation and to a geometrical distortion. Our results establish Rydberg atom arrays as a promising platform for the preparation and microscopic characterization of quantum spin liquid candidates.
We theoretically analyze recent experiments [Semeghini et al., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase-the resonating valence bond state of hard dimers-in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.
Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum Monte Carlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wave functions. These blockaded models include both creation or annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterization of spin liquid states.
The recent experimental detection of the onset of a dynamically prepared, gapped Z_{2} quantum spin liquid on the ruby lattice brought the physics of frustrated magnetism and lattice gauge theory to Rydberg tweezer arrays [Semeghini et al., Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794]. The thermodynamic properties of such models remain inadequately addressed, yet knowledge thereof is indispensable if one wants to prepare large, robust, and long-lived quantum spin liquids. Using large scale quantum Monte Carlo simulations we find in the PXP model a renormalized classical spin liquid with constant entropy density S/N approaching ln(2)/6 in the thermodynamic limit for all moderate and large values of the detuning δ and starting from T/Ω∼0.5 (in units of the Rabi frequency Ω) down to the lowest temperatures we could simulate, T/Ω∼0.01. With van der Waals interactions, constant entropy plateaus are still found but its value shifts with δ. We comment on the implications of the adiabatic approximation to the dynamical ramps for the electric degrees of freedom, which leads to a reinterpretation of the experimental observations.
Topological entanglement entropy (TEE) provides a universal measure of long-range quantum correlations in topologically ordered systems, offering critical insights into exotic phases of matter. While theoretical frameworks, including exactly solvable lattice models, tensor networks, and field-theoretic approaches, enable precise computation of TEE in idealized settings, practical implementation faces multiple challenges. Finite-size and geometry effects, including boundary corners and lattice discretization, introduce significant corrections that can obscure the small topological contribution. Gapless edges in chiral topological phases further complicate the isolation of bulk entanglement, requiring careful separation of edge and bulk contributions. Symmetry-protected and symmetry-enriched phases necessitate additional diagnostics, such as symmetry-resolved entanglement and entanglement negativity, to fully characterize topological properties. Experimental measurement remains challenging, with current approaches limited to small systems using Rényi entropies via swap operations and interferometric methods. This work synthesizes these practical considerations, outlines mitigation strategies, and highlights ongoing directions for bridging theoretical, numerical, and experimental approaches to robustly quantify TEE. Understanding these limitations is essential for accurate characterization of topological order and for guiding the development of quantum technologies leveraging topological protection.