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arXiv:2507.17386 · Physical Review Letters

Symmetry Rebreaking in an Effective Theory of Quantum Coarsening

Federico Balducci, Anushya Chandran, Roderich Moessner

Published Dec 22, 2025• 2 citations
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Abstract

We present a simple theory accounting for two central observations in a recent experiment on quantum coarsening and collective dynamics on a programmable quantum simulator [Manovitz et al., Nature (London) 638, 86 (2025).NATUAS0028-083610.1038/s41586-024-08353-5]: an apparent speeding up of the coarsening process as the phase transition is approached and persistent oscillations of the order parameter after quenches within the ordered phase. Our theory, based on the Hamiltonian structure of the equations of motion in the classical limit of the quantum model, finds a speeding up already deep within the ordered phase, with subsequent slowing down as the domain wall tension vanishes upon approaching the critical line. Further, the oscillations are captured within a mean-field treatment of the order parameter field. For quenches within the ordered phase, small spatially varying fluctuations in the initial mean field lead to a remarkable long-time effect, wherein the system dynamically destroys its long-range order and has to coarsen to re-establish it. We term this phenomenon symmetry rebreaking, as the resulting late-time magnetization can have a sign opposite to the initial magnetization.

DOI
10.1103/q1lm-99z4

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We present a simple theory accounting for two central observations in a recent experiment on quantum coarsening and collective dynamics on a programmable quantum simulator [Manovitz et al., Nature (London) 638, 86 (2025).NATUAS0028-083610.1038/s41586-024-08353-5]: an apparent speeding up of the coarsening process as the phase transition is approached and persistent oscillations of the order parameter after quenches within the ordered phase. Our theory, based on the Hamiltonian structure of the equations of motion in the classical limit of the quantum model, finds a speeding up already deep within the ordered phase, with subsequent slowing down as the domain wall tension vanishes upon approaching the critical line. Further, the oscillations are captured within a mean-field treatment of the order parameter field. For quenches within the ordered phase, small spatially varying fluctuations in the initial mean field lead to a remarkable long-time effect, wherein the system dynamically destroys its long-range order and has to coarsen to re-establish it. We term this phenomenon symmetry rebreaking, as the resulting late-time magnetization can have a sign opposite to the initial magnetization.
Understanding the collective quantum dynamics of non-equilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter1, fundamental high-energy processes2, quantum metrology3,4 and quantum algorithms5. Here we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)-dimensional Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains6. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (‘Higgs’) mode7. These observations offer a viewpoint into emergent collective dynamics in strongly correlated quantum systems and non-equilibrium quantum processes. A programmable quantum simulator based on Rydberg atom arrays is used to study the collective dynamics of a quantum phase transition and observe the phenomenon of quantum coarsening.
The phase-ordering dynamics that results from domain coarsening is considered for itinerant quantum ferromagnets. The fluctuation effects that invalidate the Hertz theory of the quantum phase transition also affect the phase ordering. For a quench into the ordered phase, there appears a transient regime where the domain growth follows a different power law than in the classical case, and for asymptotically long times, the prefactor of the t1∕2{t}^{1∕2}t1∕2 growth law has an anomalous magnetization dependence. A quench to the quantum critical point results in a growth law that is not a power-law function of time. Both phenomenological scaling arguments and renormalization-group arguments are given to derive these results, and estimates of experimentally relevant length and time scales are presented.
Several mean-field computations have revealed the existence of an out-of-equilibrium dynamical transition induced by quantum-quenching an isolated system starting from its symmetry-broken phase. In this work we focus on the quantum ${\ensuremath{\phi}}^{4}$ NNN-component field theory. By taking into account dynamical fluctuations at the Hartree-Fock level, corresponding to the leading order of the 1/N1/N1/N expansion, we derive the critical properties of the dynamical transition beyond mean-field theory (including at finite temperature). We find diverging time and length scales, dynamic scaling, and aging. Finally, we unveil a relationship with critical coarsening, an off-equilibrium regime that can be induced by quenching from the symmetric toward the symmetry-broken phase.
The nonequilibrium dynamics of a system that is located in the vicinity of a quantum critical point is affected by the critical slowing down of order-parameter correlations with the potential for novel out-of-equilibrium universality. After a quantum quench, i.e., a sudden change of a parameter in the Hamiltonian, such a system is expected to almost instantly fall out of equilibrium and undergo aging dynamics, i.e., dynamics that depends on the time passed since the quench. Investigating the quantum dynamics of an NNN-component ${\ensuremath{\varphi}}^{4}$ model coupled to an external bath, we determine this universal aging and demonstrate that the system undergoes a coarsening, governed by a critical exponent that is unrelated to the equilibrium exponents of the system. We analyze this behavior in the large-NNN limit, which is complementary to our earlier renormalization-group analysis, allowing in particular the direct investigation of the order-parameter dynamics in the symmetry-broken phase and at the upper critical dimension. By connecting the long-time limit of fluctuations and response, we introduce a distribution function that shows that the system remains nonthermal and exhibits quantum coherence even on long time scales.
The quantum O(N)O(N)O(N) model in the infinite-NNN limit is a paradigm for symmetry breaking. Qualitatively, its phase diagram is an excellent guide to the equilibrium physics for more realistic values of NNN in varying spatial dimensions (d>1d>1d>1). Here, we investigate the physics of this model out of equilibrium, specifically its response to global quenches starting in the disordered phase. If the model were to exhibit equilibration, the late-time state could be inferred from the finite-temperature phase diagram. In the infinite-NNN limit, we show that not only does the model not lead to equilibration on account of an infinite number of conserved quantities, it also does not relax to a generalized Gibbs ensemble (GGE) consistent with these conserved quantities. Instead, an infinite number of new conservation laws emerge at late times and the system relaxes to an emergent GGE consistent with these. Nevertheless, we still find that the late-time states following quenches bear strong signatures of the equilibrium phase diagram. Notably, we find that the model exhibits coarsening to a nonequilibrium critical state only in dimensions d>2d>2d>2, that is, if the equilibrium phase diagram contains an ordered phase at nonzero temperatures.
Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.