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arXiv:2603.20372

One-to-one quantum simulation of the low-dimensional frustrated quantum magnet TmMgGaO$_4$ with 256 qubits

Lucas Leclerc, Sergi Julià-Farré, Gabriel Silva Freitas, Guillaume Villaret, Boris Albrecht, Lucas Béguin, Lilian Bourachot, Clémence Briosne-Frejaville, Dorian Claveau, Antoine Cornillot, Julius de Hond, Djibril Diallo, Clément Dupays, Robin Dupont, Thomas Eritzpokhoff, Emmanuel Gottlob, Loïc Henriet, Michael Kaicher, Lucas Lassablière, Arvid Lindberg, Yohann Machu, Hadriel Mamann, Thomas Pansiot, Julien Ripoll, Eun Sang Choi, Adrien Signoles, Joseph Vovrosh, Bruno Ximenez, Vivien Zapf, Shengzhi Zhang, Haidong Zhou, Minseong Lee, Tiagos Mendes-Santos, Constantin Dalyac, Antoine Browaeys, Alexandre Dauphin

quant-phcond-mat.mtrl-sciSubmitted Mar 20, 2026• Announced Mar 24, 2026• 0 citations
v1 · Mar 20, 2026v2 · Mar 25, 2026v3 · Apr 28, 2026
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Abstract

Low-dimensional materials exhibit exotic properties due to enhanced quantum fluctuations, making the understanding of their microscopic origin central in condensed matter physics. Analogue quantum simulators offer a powerful approach for investigating these systems at the microscopic level, particularly in large-scale regimes where quantum entanglement limits classical numerical methods. To date, analogue simulators have largely focused on universal Hamiltonians rather than material-specific quantitative comparisons. Here we use a Rydberg-based quantum simulator to study the bulk-layered frustrated quantum magnet TmMgGaO$_4$. Magnetisation measurements obtained from the quantum simulator show excellent agreement with independent measurements performed in a magnetic laboratory facility, validating the proposed effective two-dimensional microscopic Hamiltonian. Building on this quantitative correspondence, we investigate on both platforms the antiferromagnetic phase transition. We further probe the role of quantum fluctuations via snapshot analysis, connecting our results to integrated inelastic neutron scattering data. Finally, we access, with the simulator, non-equilibrium dynamics on picosecond material timescales, including frequency response and thermalisation of observables.

Comments
20 pages, 15 figures

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One-to-one quantum simulation of the low-dimensional frustrated quantum magnet TmMgGaO4_44​ with 256 qubits
Low-dimensional materials exhibit exotic properties due to enhanced quantum fluctuations, making the understanding of their microscopic origin central in condensed matter physics. Analogue quantum simulators offer a powerful approach for investigating these systems at the microscopic level, particularly in large-scale regimes where quantum entanglement limits classical numerical methods. To date, analogue simulators have largely focused on universal Hamiltonians rather than material-specific quantitative comparisons. Here we use a Rydberg-based quantum simulator to study the bulk-layered frustrated quantum magnet TmMgGaO4_44​. Magnetisation measurements obtained from the quantum simulator show excellent agreement with independent measurements performed in a magnetic laboratory facility, validating the proposed effective two-dimensional microscopic Hamiltonian. Building on this quantitative correspondence, we investigate on both platforms the antiferromagnetic phase transition. We further probe the role of quantum fluctuations via snapshot analysis, connecting our results to integrated inelastic neutron scattering data. Finally, we access, with the simulator, non-equilibrium dynamics on picosecond material timescales, including frequency response and thermalisation of observables.
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How quantum matter relaxes far from equilibrium is a central open problem in many-body physics, and one for which analog quantum simulators are well positioned to move from confirming theory to discovering new physics. Here, we use a two-dimensional Rydberg atom array of 256 qubits to map the relaxation landscape of the two-dimensional transverse-field Ising model across its phase diagram. Beyond the expected rapid thermalization, we identify two further regimes. The first is a prethermal regime whose dynamics are governed by an effective XY model. The second, and most unexpected, is a crossover regime characterized by a slowdown in relaxation. This slowdown occurs precisely where state-of-the-art classical tensor-network methods lose control at late times, whereas the quantum simulation remains consistent across system sizes. These results establish Rydberg atom arrays as a platform for scientific discovery in nonequilibrium quantum many-body dynamics.
Abstract Frustrated magnets hold the promise of material realizations of exotic phases of quantum matter, but direct comparisons of unbiased model calculations with experimental measurements remain very challenging. Here we design and implement a protocol of employing many-body computation methodologies for accurate model calculations—of both equilibrium and dynamical properties—for a frustrated rare-earth magnet TmMgGaO 4 (TMGO), which explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz–Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex–antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics, and we further propose experimental detection of its intriguing properties.
Frustrated magnets host rich emergent behavior because competing interactions generate dense manifolds of low-energy states. The Ising Shastry-Sutherland model is a paradigmatic setting, motivated experimentally by Ising-like rare-earth tetraborides such as TmB4_44​ and ErB4_44​, whose field-induced magnetization plateaus have motivated extensive microscopic modeling. Yet how tunable quantum fluctuations reorganize this material-motivated phase diagram remains largely unexplored. Here, we realize a transverse- and longitudinal-field Ising model on the Shastry-Sutherland lattice using a programmable Rydberg-atom array. We map its quantum phase diagram using density matrix renormalization group calculations and probe corresponding signatures experimentally in arrays containing more than 110 atoms. Beyond the established classical phases, the calculations identify two regimes absent in the classical limit and stabilized at finite transverse field: a 2/52/52/5 filling plateau whose finite stability region emerges from a classically degenerate phase boundary and a symmetry-preserving quantum-dimer regime replacing classically selected collinear order. Experiments on finite open arrays reveal signatures consistent with these regimes across three boundary-pinning conditions, with the resulting response maps agreeing qualitatively with the calculated phase diagram. Our results establish programmable Rydberg-atom arrays as tools for exploring frustrated, material-motivated Hamiltonians and motivate searches for new, quantum-driven magnetization plateaus and quantum-dimer behavior in ErB4_44​ under a transverse field or in strain-tuned TmB4_44​.
Geometric frustration in two-dimensional Ising models allows for a wealth of exotic universal behavior, both Ising and non-Ising, in the presence of quantum fluctuations. In particular, the triangular antiferromagnet and Villain model in a transverse field can be understood through distinct XY pseudospins, but have qualitatively similar phase diagrams including a quantum phase transition in the (2+1)-dimensional XY universality class. While the quantum dynamics of modestly-sized systems can be simulated classically using tensor-based methods, these methods become infeasible for larger lattices. Here we perform both classical and quantum simulations of these dynamics, where our quantum simulator is a superconducting quantum annealer. Our observations on the triangular lattice suggest that the dominant quench dynamics are not described by the quantum Kibble-Zurek scaling of the quantum phase transition, but rather a faster coarsening dynamics in an effective two-dimensional XY model in the ordered phase. Similarly, on the Villain model, the scaling exponent does not match the Kibble-Zurek expectation. These results demonstrate the ability of quantum annealers to perform coherent quantum dynamics simulations that are hard to classically scale beyond small systems, and open the avenue to predictive simulations of the dynamics of Ising magnetic materials on quantum simulators.
The Ghost of a Vanishing Stripe Order in the Triangular Quantum Ising Magnet TmMgGaO4_44​
Frustrated magnets host the promises of material realizations of new paradigm of quantum matter, while direct comparison of unbiased model calculations with experimental measurements is still very challenging. Here, we design and implement a protocol of employing many-body computation methodologies for accurate model calculation -- both equilibrium and dynamical properties -- of a frustrated rare-earth magnet TmMgGaO4_44​ (TMGO), which perfectly explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz-Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex-antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics and we further propose experimental detections of its intriguing properties.