Role of Lattice Geometry and Hamiltonian Engineering in the Universality of Spin Squeezing Dynamical Phase Transitions

Recent works have established the dynamical generation of entanglement in the form of two-mode squeezing in power-law interacting spin-1/2 bilayer XXZ models. Furthermore, a dynamical phase transition, separating a fully collective squeezing phase from a partially collective phase with universal critical scaling, has been demonstrated within the same models. In this work, we extend this framework to explore how different lattice geometries affect the nonequilibrium dynamics. Focusing on bilayer systems with square, honeycomb, and triangular lattices, we investigate the role of different lattice geometries on the dynamical transition and the universal critical scaling of the squeezing phase.

Additionally, unlike modifying the interlayer separation as done in the previous works, we introduce a more experimentally accessible control parameter in the ratio between interlayer and intralayer interactions. Using Floquet protocol to vary the interlayer coupling strength, while keeping the layer spacing fixed, we demonstrate that the dynamical transition can be driven purely through interaction engineering. This approach enables practical access to the transition without modifying the underlying geometry or aspect ratios.

These findings provide a versatile route toward controlling entanglement generation in Rydberg arrays, polar molecules, and trapped-ion platforms with applications in quantum sensing and simulation.