Universal Spin Squeezing Dynamical Phase Transitions across Lattice Geometries, Dimensions, and Microscopic Couplings

TL;DR

This paper demonstrates the universality of a dynamical spin squeezing phase transition across various lattice geometries, dimensions, and interaction couplings, supported by theoretical and simulation analyses.

Contribution

It establishes the non-equilibrium universality class of the transition across different geometries and coupling regimes, with analytical scaling laws derived.

Findings

Transition persists across all studied lattice geometries and coupling ratios.

Critical exponents are consistent within error across different geometries.

Analytical scaling laws for the critical aspect ratio are derived for different interaction regimes.

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.