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This study establishes the universality of dynamical spin squeezing phase transitions across diverse lattice geometries and interaction strengths in bilayer XXZ models. By confirming that these non-equilibrium critical behaviors persist regardless of specific lattice topology or coupling scaling, the work provides a robust theoretical framework for controlling entanglement generation in quantum simulation platforms like Rydberg arrays and trapped ions. These findings are significant for advancing precision quantum sensing and simulation capabilities by demonstrating that such transitions can be engineered through interaction tuning rather than geometric modification.
Universal Spin Squeezing Dynamical Phase Transitions across Lattice Geometries, Dimensions, and Microscopic Couplings
arXiv:2605.13969v2 Announce Type: replace Abstract: 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 $2\mathrm{D}$ bilayers as well as $1\mathrm{D}$ ladders, and a symmetry-preserving rescaling $\lambda$ 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 $\lambda$ with critical exponents consistent within error, providing strong evidence for a genuine non-equilibrium universality class. The Bogoliubov theory recovers the previously identified scaling $a_Z^* \propto L$ in the long-range interacting regime $\alpha d+2$, with $\alpha$ the power-law exponent in dimension $d$. This uncovers a previously unrecognized sub-linear regime for short-range interactions. By tuning $\lambda$ 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.
Abstract: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 $2\mathrm{D}$ bilayers as well as $1\mathrm{D}$ ladders, and a symmetry-preserving rescaling $\lambda$ 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 $\lambda$ with critical exponents consistent within error, providing strong evidence for a genuine non-equilibrium universality class. The Bogoliubov theory recovers the previously identified scaling $a_Z^* \propto L$ in the long-range interacting regime $\alpha < d+2$, and yields an analytical scaling $a_Z^* \propto L^{2/(\alpha-d)}$ for the critical aspect ratio with system size for $\alpha>d+2$, with $\alpha$ the power-law exponent in dimension $d$. This uncovers a previously unrecognized sub-linear regime for short-range interactions. By tuning $\lambda$ 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.
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas)
arXiv:2605.13969 [quant-ph]
(or arXiv:2605.13969v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2605.13969 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.1103/py4q-klzp Focus to learn more DOI(s) linking to related resources
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