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arXiv:2608.07211

Observation of far-from-equilibrium scaling in the transient dynamics of 2D quantum magnets

Fabio Bensch, Umberto Borla, Federico Balducci, Philip Osterholz, Shuanghong Tang, Silpa Baburaj Sheela, Anushya Chandran, Roderich Moessner, Jad C. Halimeh, Christian Groß

cond-mat.quant-gasquant-phSubmitted Aug 7, 2026• Announced Aug 10, 2026• 0 citations
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Abstract

The transient regime of far-from-equilibrium quantum many-body dynamics lacks the established organizing principles that universality and scaling provide in equilibrium. It is least understood for two-dimensional short-range interacting systems, where mean-field arguments are not expected to hold, controlled theoretical descriptions are few, and fluctuations are strong. Here we investigate the quench dynamics of the transverse-field Ising model using programmable Rydberg-atom arrays realizing honeycomb, square, kagome, and triangular lattices. Starting from a fully magnetized state, we observe a pronounced softening of the dominant collective magnetization oscillation accompanied by a maximum in the damping rate, signaling a crossover between interaction- and field-dominated transient dynamics. Even though the microscopic lattice geometries are different, both the oscillation frequencies and the damping rates collapse onto common curves after being rescaled by the coordination-number-weighted interaction strength. Our findings show that a mean-field description effectively reproduces the magnetization oscillations. The importance of correlated quantum fluctuations is underlined by the failure of the discrete truncated Wigner approximation to predict the damping for strong interactions, while tree-tensor-network simulations reproduce the dynamics accurately. These results reveal a robust scaling regime governing the transient dynamics of short-range interacting two-dimensional quantum magnets. They reveal that the dominant transient dynamics is governed by a simple collective description despite the presence of strong quantum fluctuations --- an important insight in the quest to uncover organizing principles in far-from-equilibrium quantum matter.

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Dynamical detection of quantum phases and phase transitions (QPTs) in quenched systems with experimentally convenient initial states is a topic of interest from both theoretical and experimental perspectives. Quenched from polarized states, longitudinal magnetization decays exponentially to zero in time for the short-range transverse-field Ising model and hence has a featureless steady state regime, which prevents it from exhibiting dynamical phase transitions of type I. In this paper, we ask whether the transient regimes of such nonequilibrium processes probed by single-site observables, that is magnetization per site, could encode information about the underlying QPT. The decay rates of time-dependent and single-site observables exhibit a dynamical crossover that separates two dynamical regions, ordered and disordered, both of which have distinct nonequilibrium responses. We construct a dynamical order parameterlike quantity that exhibits a scaling law in the vicinity of the crossover. Our results reveal that scaling law exponent in short times in the close vicinity of the dynamical crossover is significantly different than the one predicted by analytical theory for long times. When integrability is strongly broken, the crossover boundary turns into a region that separates two other dynamical regions that act like dynamically ordered and disordered regimes.

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The transient regime of far-from-equilibrium quantum many-body dynamics lacks the established organizing principles that universality and scaling provide in equilibrium. It is least understood for two-dimensional short-range interacting systems, where mean-field arguments are not expected to hold, controlled theoretical descriptions are few, and fluctuations are strong. Here we investigate the quench dynamics of the transverse-field Ising model using programmable Rydberg-atom arrays realizing honeycomb, square, kagome, and triangular lattices. Starting from a fully magnetized state, we observe a pronounced softening of the dominant collective magnetization oscillation accompanied by a maximum in the damping rate, signaling a crossover between interaction- and field-dominated transient dynamics. Even though the microscopic lattice geometries are different, both the oscillation frequencies and the damping rates collapse onto common curves after being rescaled by the coordination-number-weighted interaction strength. Our findings show that a mean-field description effectively reproduces the magnetization oscillations. The importance of correlated quantum fluctuations is underlined by the failure of the discrete truncated Wigner approximation to predict the damping for strong interactions, while tree-tensor-network simulations reproduce the dynamics accurately. These results reveal a robust scaling regime governing the transient dynamics of short-range interacting two-dimensional quantum magnets. They reveal that the dominant transient dynamics is governed by a simple collective description despite the presence of strong quantum fluctuations --- an important insight in the quest to uncover organizing principles in far-from-equilibrium quantum matter.
Strongly interacting many-body systems exhibit collective properties that emerge from complex correlations among microscopic degrees of freedom. These cooperative phenomena govern the non-equilibrium response of quantum systems, with relevance ranging from condensed matter physics to quantum field theories describing fundamental aspects of our universe. Understanding such emergent dynamics from first principles remains one of the central challenges in quantum many-body physics. Here we report on the observation of collective cluster nucleation dynamics following quenches in 2D ferromagnetic quantum Ising systems implemented in an atomic Rydberg array. Our experiments reveal two distinct regimes: In the confined regime, we observe an energy-dependent cluster size, revealing large collective clusters exceeding ten spins. In contrast, the deconfined regime is characterized by kinetically constrained, avalanche-like nucleation dynamics involving the entire system. Our findings establish a new frontier for quantum simulations with Rydberg arrays, enabling controlled exploration of non-equilibrium phenomena previously out of reach. Beyond advancing experimental capabilities, they provide fundamental insights into highly correlated processes with implications that reach from quantum magnetism and glassy dynamics to cosmological models of the early universe.
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.
By means of the discrete truncated Wigner approximation, we study dynamical phase transitions arising in the steady state of transverse-field Ising models after a quantum quench. Starting from a fully polarized ferromagnetic initial condition, these transitions separate a phase with nonvanishing magnetization along the ordering direction from a disordered symmetric phase upon increasing the transverse field. We consider two paradigmatic cases, a one-dimensional long-range model with power-law interactions $\ensuremath{\propto}1/{r}^{\ensuremath{\alpha}}$ decaying algebraically as a function of distance rrr and a two-dimensional system with short-range nearest-neighbor interactions. In the former case, we identify dynamical phase transitions for $\ensuremath{\alpha}\ensuremath{\lesssim}2$ and we extract the critical exponents from a data collapse of the steady-state magnetization for up to 1200 lattice sites. We find identical exponents for $\ensuremath{\alpha}\ensuremath{\lesssim}0.5$, suggesting that the dynamical transitions in this regime fall into the same universality class as the nonergodic mean-field limit. The two-dimensional Ising model is believed to be thermalizing, which we also confirm using exact diagonalization for small system sizes. Thus, the dynamical transition is expected to correspond to the thermal phase transition, which is consistent with our data upon comparing to equilibrium quantum Monte Carlo simulations. We further test the accuracy of the discrete truncated Wigner approximation by comparing against numerically exact methods such as exact diagonalization, tensor network, as well as artificial neural network states and we find good quantitative agreement on the accessible time scales. Finally, our work provides an additional contribution to the understanding of the range and the limitations of qualitative and quantitative applicability of the discrete truncated Wigner approximation.
Simulating the real-time evolution of quantum spin systems far out of equilibrium poses a major theoretical challenge, especially in more than one dimension.We experimentally explore quench dynamics in a two-dimensional Ising spin system with transverse and longitudinal fields.We realize the system with a near unit-occupancy atomic array of over 200 atoms obtained by loading a spin-polarized band insulator of fermionic lithium into an optical lattice and induce short-range interactions by direct excitation to a lowlying Rydberg state.Using site-resolved microscopy, we probe antiferromagnetic correlations in the system after a sudden quench from a paramagnetic state and compare our measurements to numerical calculations using state-of-the-art techniques.We achieve many-body states with longer-range antiferromagnetic correlations by implementing a near-adiabatic quench of the longitudinal field and study the buildup of correlations as we vary the rate with which we change the field.
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.
Dynamical detection of quantum phases and phase transitions (QPTs) in quenched systems with experimentally convenient initial states is a topic of interest from both theoretical and experimental perspectives. Quenched from polarized states, longitudinal magnetization decays exponentially to zero in time for the short-range transverse-field Ising model and hence has a featureless steady state regime, which prevents it from exhibiting dynamical phase transitions of type I. In this paper, we ask whether the transient regimes of such nonequilibrium processes probed by single-site observables, that is magnetization per site, could encode information about the underlying QPT. The decay rates of time-dependent and single-site observables exhibit a dynamical crossover that separates two dynamical regions, ordered and disordered, both of which have distinct nonequilibrium responses. We construct a dynamical order parameterlike quantity that exhibits a scaling law in the vicinity of the crossover. Our results reveal that scaling law exponent in short times in the close vicinity of the dynamical crossover is significantly different than the one predicted by analytical theory for long times. When integrability is strongly broken, the crossover boundary turns into a region that separates two other dynamical regions that act like dynamically ordered and disordered regimes.