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arXiv:2607.22933

Emergent integrable dynamics in a non-integrable Rydberg-atom chain

Gianluca Morettini, Luca Capizzi, Leonardo Mazza, Maurizio Fagotti

cond-mat.quant-gascond-mat.stat-mechquant-phSubmitted Jul 24, 2026• Announced Jul 28, 2026• 0 citations
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Abstract

We show that integrable and non-integrable dynamics can coexist in the same Rydberg-atom chain, depending on the initial state in which the system is prepared. In the setting we consider, Rydberg atoms mainly experience an effective dipolar interaction and, within the nearest-neighbor approximation, their dynamics can be mapped onto an effective integrable Fermi gas with ballistic transport. The inclusion of longer-range couplings, however, is essential for the theory to be predictive; those terms break the conservation laws associated with integrability, enabling, in particular, the emergence of genuine diffusive transport. We study the dynamics generated by a bipartition protocol and reveal a sharp qualitative change in behavior as the particle density is varied, suggesting the possibility of accessing weaker and stronger integrability breaking dynamics in the same Hamiltonian depending on the relevance of local interactions. We propose a theoretical mechanism that accounts for the differences. Our findings provide clear and concrete evidence that integrability breaking is not solely a property of the Hamiltonian and of the magnitude of the couplings that break integrability, but also of the state in which the system is prepared.

Comments
4.5 pages + End Matter, 3 figures

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We show that integrable and non-integrable dynamics can coexist in the same Rydberg-atom chain, depending on the initial state in which the system is prepared. In the setting we consider, Rydberg atoms mainly experience an effective dipolar interaction and, within the nearest-neighbor approximation, their dynamics can be mapped onto an effective integrable Fermi gas with ballistic transport. The inclusion of longer-range couplings, however, is essential for the theory to be predictive; those terms break the conservation laws associated with integrability, enabling, in particular, the emergence of genuine diffusive transport. We study the dynamics generated by a bipartition protocol and reveal a sharp qualitative change in behavior as the particle density is varied, suggesting the possibility of accessing weaker and stronger integrability breaking dynamics in the same Hamiltonian depending on the relevance of local interactions. We propose a theoretical mechanism that accounts for the differences. Our findings provide clear and concrete evidence that integrability breaking is not solely a property of the Hamiltonian and of the magnitude of the couplings that break integrability, but also of the state in which the system is prepared.
Integrable quantum many-body systems host families of extensive conservation laws, some of which are fragile: even infinitesimal perturbations can qualitatively alter their dynamical constraints. Here we show that this fragility leaves a clear experimental fingerprint in a one-dimensional quantum spin chain of as few as 14 Rydberg atoms. Weak integrability breaking from interatomic dipolar couplings is directly detectable within experimentally accessible times in the dynamics of non-local observables. In particular, magnetization fluctuations are highly sensitive to the breaking of fragile conservation laws and exhibit anomalous growth, which we observe experimentally; similar signatures appear in a semilocal string observable. Numerical simulations on substantially longer chains and a simplified classical stochastic model reproduce those features. We establish non-local observables as a sensitive probe of fragile conservation laws in quantum spin chains and Rydberg-atom arrays as a platform to test perturbative descriptions of quantum many-body dynamics with weak integrability breaking.
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We present a theoretical investigation into the expansion dynamics of Rydberg-dressed ultracold Fermi gases. The effective interaction potential induced by Rydberg dressing significantly modifies the intrinsic properties and dynamical behavior of the quantum gas. The strength and range of these interactions can be precisely tuned by varying the intensity and detuning of the applied laser field. By employing mean-field theory and utilizing the density distribution of the atomic cloud to describe the quantum system dynamics, we theoretically describe the time-dependent evolution of the atomic cloud during the free expansion process, encompassing both non-interacting and unitary Fermi gases. Notably, the specific quantum states of the ground-state atoms play a pivotal role in shaping the effective interaction potential within the Rydberg-dressed quantum system. We elucidate how the interaction potential influences the rate and mode of the atom cloud’s expansion by hydrodynamic expansion arising from Rydberg-dressed atoms in distinct spin hyperfine states. This investigation may deepen our understanding of the behavior and interactions in quantum many-body systems and offer broad potential for future applications like the exploration of novel quantum phase transitions and emergent phenomena.
We study transport of local magnetization in a Heisenberg spin-1/2 chain at zero temperature. The system is initially prepared in a highly excited pure state far from equilibrium and its evolution is analyzed via exact diagonalization. Integrable and nonintegrable regimes are obtained by adjusting the parameters of the Hamiltonian, which allows for the comparison of transport behaviors in both limits. In the presence of nearest-neighbor interactions only, the transport behavior in the integrable clean system contrasts with the chaotic chain with on-site defects, oscillations in the first suggesting ballistic transport, and a fast decay in the latter indicating diffusive transport. The results for a nonintegrable system with frustration are less conclusive, similarities with the integrable chain being verified. We also show how methods of quantum control may be applied to chaotic systems to induce a desired transport behavior, such as that of an integrable system.
String breaking is one of the most representative non-perturbative dynamics processes in confinement theory, typically associated with the creation of particle-antiparticle pairs. In this paper, we take a one-dimensional Rydberg atomic chain to theoretically study the dynamical of finite-length string state. Under different string tension conditions, we find that the string dynamics exhibits two clearly distinguishable evolution characteristics: one is that the string breaks and the system enters a superposition state space containing multiple meson state configurations; the other is localized string dynamics, in which the string undergoes local breaking but can then recombine and return to a state close to the initial structure, with the breaking and recombination processes recurring over a long time scale. Through the analysis of the evolution of different meson state configurations, we visually depict the redistribution of configuration weights during the string breaking process, and reveal the observable recovery characteristics of the string after breaking. Further analysis shows that the enhancement of quantum fluctuations can increase the weight of the double-meson state configurations in the system wave function without changing the dominant dynamical behavior. The above results present a rich picture of string breaking dynamics in a one-dimensional Rydberg atomic chain and provide insights for studying confinement physics and related gauge field theory phenomena on quantum simulation platforms.
In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium one-dimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the steady state induced by thermal boundary driving in a XXZ spin chain with staggered magnetic field. By means of efficient large-scale matrix product simulations of the equation of motion of the system, we calculate its steady state in the long-time limit. We start by discussing the energy transport supported by the system, finding it to be ballistic in the integrable limit and diffusive when the staggered field is finite. Subsequently, we examine the reduced density operators of neighboring sites and find that for large systems they are well approximated by local thermal states of the underlying Hamiltonian in the nonintegrable regime, even for weak staggered fields. In the integrable limit, on the other hand, this behavior is lost, and the identification of local temperatures is no longer possible. Our results agree with the intuitive connection between energy diffusion and thermalization.