Towards spin-squeezing in two-dimensional ensembles of solid-state defects

Generating spin-squeezed states in quantum simulators with power-law interactions is a key experimental challenge with limited theoretical guidance. While numerical evidence suggests it should be possible to achieve spin squeezing with sufficiently long-range (but still energetically extensive) XXZ Hamiltonians, the precise requirements remain unclear. We conjecture an explanation for the "squeezing phase diagram" of long-range XXZ models. While squeezing in such models is dynamically generated by time evolution from simple product states, our explanation is intimately connected to the presence of finite-temperature equilibrium order in the Hamiltonian. Using a variety of numerical methods, we test our conjecture in one-dimensional models and find necessary and sufficient conditions for spin squeezing. We discuss the implications of these conditions for realizing spin-squeezing in a two-dimensional ensemble of solid-state defects coupled via magnetic dipole-dipole interactions.