Long-range spin-spin interactions are known to generate nonequilibrium dynamics that can squeeze the collective spin of a quantum spin ensemble in a scalable manner, leading to states whose metrologically useful entanglement grows with system size. Here, we show theoretically that scalable squeezing can be produced in 2D U(1)-symmetric systems even by short-range interactions, i.e., interactions that at equilibrium do not lead to long-range order at finite temperatures, but rather to an extended Berezinskii-Kosterlitz-Thouless critical phase. If the initial state is a coherent spin state in the easy plane of interactions, whose energy corresponds to a thermal state in the critical Berezinskii-Kosterlitz-Thouless phase, the nonequilibrium dynamics exhibits critical slowing down, corresponding to a power-law decay of the collective magnetization in time. This slow decay protects scalable squeezing, whose scaling reveals in turn the decay exponent of the magnetization. Our results open the path to realizing massive entangled states of potential metrological interest in many relevant platforms of quantum simulation and information processing-such as Mott insulators of ultracold atoms, or superconducting circuits-characterized by short-range interactions in planar geometries.
Controlling the quantum many-body state of arrays of qudits, possessing a large local Hilbert space, opens the path to a broad range of possibilities for many-particle entanglement, interesting both for fundamental quantum science, as well as for potential metrological applications. In this work we theoretically show that the spin-spin interactions realized in two-dimensional Mott insulators of large-spin magnetic atoms (such as Cr, Er or Dy) lead to scalable spin squeezing along the non-equilibrium unitary evolution initialized in a coherent spin state. An experimentally relevant perturbation to the collective squeezing dynamics is offered by a quadratic Zeeman shift, which leads instead to squeezing of individual spins. Making use of a truncated cumulant expansion for the quantum fluctuations of the spin array, we show that, for sufficiently small quadratic shifts, the spin squeezing dynamics is akin to that produced by the paradigmatic one-axis-twisting (OAT) model -- as expected from an effective separation between collective spin and spin-wave variables. Spin squeezing with OAT-like scaling is shown to be protected by the robustness of long-range ferromagnetic order to quadratic shifts in the equilibrium phase diagram of the system, that we reconstruct via quantum Monte Carlo and mean-field theory.
We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local
su(D) exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling
ξ2∝1/N in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.
We theoretically show that the spin-spin interactions realized in two-dimensional Mott insulators of large-spin magnetic atoms (such as Cr, Er, or Dy) lead to scalable spin squeezing along the nonequilibrium unitary evolution initialized in a coherent spin state. An experimentally relevant perturbation to the collective squeezing dynamics is offered by a quadratic Zeeman shift, which leads instead to squeezing of individual spins. Making use of a truncated cumulant expansion for the quantum fluctuations of the spin array, we show that, for sufficiently small quadratic shifts, the spin squeezing dynamics is akin to that produced by the paradigmatic one-axis-twisting model-as expected from an effective separation between collective-spin and spin-wave variables. Scalable spin squeezing is shown to be protected by the robustness of long-range ferromagnetic order to quadratic shifts in the equilibrium phase diagram of the system that we reconstruct via quantum Monte Carlo and mean-field theory.
We investigate phase transitions in the nonequilibrium dynamics of power-law interacting spin-1/2 bilayer XXZ models, which have recently been shown to allow generation of entanglement in the form of two-mode squeezing. We find a transition between a collective phase characterized by Heisenberg limited squeezing and a partially collective phase with scalable squeezing. We identify universal scaling of the squeezing dynamics in terms of system parameters and a divergent timescale, establishing these as distinct dynamical phases within the framework of nonequilibrium critical phenomena. Our Letter demonstrates a novel dynamical phase transition with potential applications in quantum sensing and quantum simulation in cold-atomic, molecular, or Rydberg platforms.
Recent work has identified a dynamical squeezing phase transition in power-law interacting bilayer XXZ spin models, separating a fully collective phase with Heisenberg-limited squeezing from a partially-collective phase with universal critical scaling. Here we test and establish the universality of this transition along two qualitatively different microscopic axes: lattice geometry, by studying square, triangular, and honeycomb
2D bilayers as well as
1D ladders, and a symmetry-preserving rescaling
λ of the interlayer couplings relative to the intralayer ones. Combining a Bogoliubov instability analysis with discrete truncated Wigner simulations, we find that the transition persists across all four lattice geometries and over a wide range of
λ with critical exponents consistent within error, providing strong evidence for a genuine non-equilibrium universality class. The Bogoliubov theory recovers the previously identified scaling
aZ∗∝L in the long-range interacting regime
α<d+2, and yields an analytical scaling
aZ∗∝L2/(α−d) for the critical aspect ratio with system size for
α>d+2, with
α the power-law exponent in dimension
d. This uncovers a previously unrecognized sub-linear regime for short-range interactions. By tuning
λ we vary the interlayer coupling strength at fixed layer spacing, demonstrating that the dynamical transition can be driven purely through interaction engineering without modifying the underlying geometry. These findings provide a versatile route toward controlling entanglement generation in Rydberg-array, polar molecule, and trapped-ion platforms with applications in quantum sensing and simulation.
Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (
1/rα) interactions in
D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small
α the scaling of squeezing with system size is identical to the infinite-range (
α=0) case. This indifference to the interaction range persists up to a critical value
α=2D/3, above which squeezing degrades continuously. Boundary-induced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.