Spin squeezing dynamical phase transition in the power-law XXZ model

We investigate spin squeezing dynamics in an XXZ model with interactions that fall off with distance r as 1/r^α in D=2 and 3 spatial dimensions. In stark contrast to the Ising model, we find a broad parameter regime where spin squeezing comparable to the infinite-range (α=0) limit is achievable even when interactions are short-ranged (α>D). A region of "collective" behavior in which optimal squeezing grows with system size extends all the way to the infinite-α limit of nearest-neighbor interactions. We identify this region with a dynamical phase of the power-law XXZ model, and discuss connections to thermal equilibrium and ground-state phases. Our predictions, made using the discrete truncated Wigner approximation, are testable in a variety of experimental cold atomic, molecular, and optical platforms.