A Landau Theory for Spin Squeezing*

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. Here, we conjecture a comprehensive 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 and thermalization within symmetry sectors of fixed total magnetization. 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 variety of quantum simulation platforms.