Critical opalescence across the doping-driven Mott transition in the two-dimensional fermionic Hubbard model

Phase transitions and their associated crossovers are imprinted in the behavior of fluctuations. Motivated by recent experiments on cold atoms in optical lattices, we study the thermodynamic density fluctuations δN² of the 2D Hubbard model with plaquette cellular dynamical mean-field theory. To understand the length scale of these fluctuations, we separate the local from the nonlocal contributions to δN². We determine the effects of particle statistics, interaction strength, temperature, and density. At high temperature, our theoretical framework reproduces the experimental observations in the doping-driven crossover regime between metal and Mott insulator. At low temperature, there is an increase of thermodynamic density fluctuations, analogous to critical opalescence, accompanied by a reduction of the absolute value of their nonlocal contributions. An enhancement in the energy fluctuations is also found. This is a precursory sign of an underlying transition between a pseudogap phase and a metallic phase in doped Mott insulators, which could play a key role in cuprates. We propose predictions for cold atom experiments.
Refs: C. Walsh et al., PRB 99, 165151 (2019); G. Sordi et al., PRB 100, 121105(R) (2019)