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arXiv:2512.09040 · Physical Review Letters

Optimizing the dynamical preparation of quantum spin lakes on the ruby lattice

DinhDuy Vu, Dominik S. Kufel, Jack Kemp, Lode Pollet, Chris R. Laumann, Norman Y. Yao

quant-phcond-mat.dis-nnSubmitted Dec 9, 2025• Announced Dec 11, 2025• 0 citations
v1 · Dec 9, 2025v2 · Aug 25, 2026
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Abstract

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 $γ= \ln 2$. We extract two physical length scales $λ$ and $ξ$ which constrain the extent of the quantum spin lake $\ell$ from above and below.

Journal reference
Physical Review Letters 137, 093402 (2026)
DOI
10.1103/7dnl-6kg2
Comments
15 pages, 11 figures

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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=384N=384N=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=ln⁡2γ= \ln 2γ=ln2. We extract two physical length scales λλλ and ξξξ which constrain the extent of the quantum spin lake ℓ\ellℓ from above and below.
While many-body systems can host long-ranged entangled quantum spin liquids (QSLs), the ingredients for realizing these as ground states can be prohibitively difficult. In many circumstances, one requires (i) a constrained Hilbert space and (ii) an extensive quantum superposition. The paradigmatic example is the toric code, or Z2\mathbb{Z}_2Z2​ spin liquid, which is a superposition of closed loop states. We show how non-equilibrium Hamiltonian dynamics can provide a streamlined route toward creating such QSLs. Rather than cooling into the ground state of a Hamiltonian, we show how a simple parameter sweep can dynamically project a family of initial product states into the constrained space, giving rise to a QSL. For the toric code, this is achieved in systems with a separation in energy scales between the eee- and mmm-anyons, where one can sweep in a way that is adiabatic (sudden) with respect to the former (latter). Although this separation of scales does not extend to the thermodynamic limit, we analytically and numerically show that this method efficiently prepares a spin liquid in finite-sized regions, which we brand ``quantum spin lakes.'' This mechanism elucidates recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. In fact, the slow dynamics of mmm-anyons suggest that we can capture spin lake preparation by simulating the dynamics on tree lattices, which we confirm with tensor network simulations. Finally, we use this mechanism to propose new experiments, e.g., for preparing a finite-sized U(1)U(1)U(1) spin liquid as a honeycomb Rokhsar-Kivelson dimer model using Rydberg atoms -- which is remarkable given its equilibrium counterpart is unstable in 2+12 + 12+1D. Our work opens up a new avenue in the study of non-equilibrium physics, as well as the exploration of exotic states of finite extent in NISQ devices.
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.
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.
Locally constrained gauge theories underpin our understanding of fundamental interactions in particle physics and the emergent behaviour of quantum materials. In strongly correlated systems, they can give rise to quantum spin liquids that lack conventional order and are defined by coherent superpositions of an extensive number of many-body configurations. Realising and probing such exotic states experimentally is an outstanding challenge both in solid-state and synthetic quantum systems, not least due to the difficulty of detecting the fragile coherences between many-body states. Here, we report a large-scale (>3,000 sites) realisation of a two-dimensional U(1) lattice gauge theory with ultracold atoms in a square optical superlattice and demonstrate non-equilibrium preparation of extended regions of U(1) quantum spin liquids. We demonstrate Gauss's law validity in a quench experiment, enabled by a new microscopy technique for detecting doubly occupied sites. We observe characteristic real-space correlations and momentum-space pinch points, hallmarks of the emergent U(1) gauge structure. Using round-trip interferometric protocols, we directly observe large-scale coherence between many-body configurations, providing strong evidence for quantum spin liquid regions extending over ~100 lattice sites. Our results establish non-equilibrium quantum simulation protocols as a powerful route for accessing and probing exotic, highly-entangled states beyond those hosted by the engineered Hamiltonian in thermal equilibrium.
Abstract Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological Z2{{\mathbb{Z}}}_{2}Z2​ Z 2 spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.
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.