Diagnostic for phases and quantum critical regions using deviations from the local fluctuation-dissipation theorem

We propose that the temperature dependence of a single quantity R=κ_i/δn_i², the ratio of the local compressibility to the local number fluctuations, can be used to map out the finite temperature phase diagram, diagnose the critical region around a quantum phase transition, and identify critical points belonging to different universality classes. We test our proposal using state-of-the-art large-scale quantum Monte Carlo simulations of the two-dimensional Bose Hubbard model. Our results have implications for recently developed single-site imaging experiments.