Isotropic integrable spin chains such as the Heisenberg model feature superdiffusive spin transport belonging to an as-yet-unidentified dynamical universality class closely related to that of Kardar, Parisi, and Zhang (KPZ). To determine whether these results extend to more generic one-dimensional models, particularly those realizable in quantum simulators, we investigate spin and energy transport in non-integrable, long-range Heisenberg models using state-of-the-art tensor network methods. Despite the lack of integrability and the asymptotic expectation of diffusion, for power-law models (with exponent $2 < α< \infty$ ) we observe long-lived $z=3/2$ superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions, up to times $t \sim 10^3/J$ . We conjecture that this KPZ-like transport is due to the proximity of such power-law-interacting models to the integrable family of Inozemtsev models, which we show to also exhibit KPZ-like spin transport across all interaction ranges. Finally, we consider anisotropic spin models naturally realized in Rydberg atom arrays and ultracold polar molecules, demonstrating that a wide range of long-lived, non-diffusive transport can be observed in experimental settings.Isotropic integrable spin chains such as the Heisenberg model feature superdiffusive spin transport belonging to an as-yet-unidentified dynamical universality class closely related to that of Kardar, Parisi, and Zhang (KPZ). To determine whether these results extend to more generic one-dimensional models, particularly those realizable in quantum simulators, we investigate spin and energy transport in non-integrable, long-range Heisenberg models using state-of-the-art tensor network methods. Despite the lack of integrability and the asymptotic expectation of diffusion, for power-law models (with exponent $2 < α< \infty$) we observe long-lived $z=3/2$ superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions, up to times $t \sim 10^3/J$. We conjecture that this KPZ-like transport is due to the proximity of such power-law-interacting models to the integrable family of Inozemtsev models, which we show to also exhibit KPZ-like spin transport across all interaction ranges. Finally, we consider anisotropic spin models naturally realized in Rydberg atom arrays and ultracold polar molecules, demonstrating that a wide range of long-lived, non-diffusive transport can be observed in experimental settings.

quant-pharXiv:2602.15933Feb 19, 20260 citations

Two-mode squeezing in Floquet-engineered power-law interacting spin models

Arman Duha, Thomas Bilitewski

Long-range interacting spin systems can be used to generate metrologically useful entanglement in the form of spin squeezing resulting in quantum enhanced sensitivity. This work considers power-law spin exchange interactions to generate two-mode squeezing in a bilayer geometry. It shows how spatial control over the geometry allows for achieving the same sensitivity with power-law interactions as with infinite-range interactions, and how spatially Floquet-engineered interactions allow for achieving the ultimate Heisenberg scaling of sensitivity.Long-range interacting spin systems can be used to generate metrologically useful entanglement in the form of spin squeezing resulting in quantum enhanced sensitivity. This work considers power-law spin exchange interactions to generate two-mode squeezing in a bilayer geometry. It shows how spatial control over the geometry allows for achieving the same sensitivity with power-law interactions as with infinite-range interactions, and how spatially Floquet-engineered interactions allow for achieving the ultimate Heisenberg scaling of sensitivity.

arXiv:2402.18642Physical Review AJun 26, 20247 citations

Asymptotic behavior of the Heisenberg model with long-range interaction

B. V. Moshchinskii, V. K. Fedyanin

Theoretical and Mathematical PhysicsApr 1, 19775 citations

Monitored long-range interacting systems: spin-wave theory for quantum trajectories

Zejian Li, Anna Delmonte, Xhek Turkeshi +1 more

Measurement-induced phases exhibit unconventional dynamics as emergent collective phenomena, yet their behavior in tailored interacting systems - crucial for quantum technologies - remains less understood. We develop a systematic toolbox to analyze monitored dynamics in long-range interacting systems, relevant to platforms like trapped ions and Rydberg atoms. Our method extends spin-wave theory to general dynamical generators at the quantum trajectory level, enabling access to a broader class of states than approaches based on density matrices. This allows efficient simulation of large-scale interacting spins and captures nonlinear dynamical features such as entanglement and trajectory correlations. We showcase the versatility of our framework by exploring entanglement phase transitions in a monitored spin system with power-law interactions in one and two dimensions, where the entanglement scaling changes from logarithm to volume law as the interaction range shortens, and by dwelling on how our method mitigates experimental post-selection challenges in detecting monitored quantum phases.Measurement-induced phases exhibit unconventional dynamics as emergent collective phenomena, yet their behavior in tailored interacting systems - crucial for quantum technologies - remains less understood. We develop a systematic toolbox to analyze monitored dynamics in long-range interacting systems, relevant to platforms like trapped ions and Rydberg atoms. Our method extends spin-wave theory to general dynamical generators at the quantum trajectory level, enabling access to a broader class of states than approaches based on density matrices. This allows efficient simulation of large-scale interacting spins and captures nonlinear dynamical features such as entanglement and trajectory correlations. We showcase the versatility of our framework by exploring entanglement phase transitions in a monitored spin system with power-law interactions in one and two dimensions, where the entanglement scaling changes from logarithm to volume law as the interaction range shortens, and by dwelling on how our method mitigates experimental post-selection challenges in detecting monitored quantum phases.

arXiv:2405.12124Nature CommunicationsMay 9, 202514 citations

2 < α< \infty

) we observe long-lived

z=3/2

superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions, up to times

t \sim 10^3/J

. We conjecture that this KPZ-like transport is due to the proximity of such power-law-interacting models to the integrable family of Inozemtsev models, which we show to also exhibit KPZ-like spin transport across all interaction ranges. Finally, we consider anisotropic spin models naturally realized in Rydberg atom arrays and ultracold polar molecules, demonstrating that a wide range of long-lived, non-diffusive transport can be observed in experimental settings.