Forestalled phase separation as the precursor to stripe order

Stripe order is a prominent feature in the phase diagram of the cuprate superconductors and has been established as the lowest-energy state of the two-dimensional Fermi-Hubbard model in relevant regimes. As temperature rises, stripes and superconductivity give way to the interesting strange-metal and pseudogap regimes. Here we investigate a crucial aspect of these regimes using numerical simulations of the square lattice Hubbard model. Using infinite projected entangled pair states with purification in the thermodynamic limit, we show that the thermodynamic charge susceptibility develops a broad maximum above the stripe regime at filling near n = 0.90, that strengthens upon cooling. Minimally entangled typical thermal states on finite cylinders attribute this enhancement to the emergence of large, fluctuating charge clusters, while the charge susceptibility remains finite. Upon further cooling, the cluster sizes stop broadening and lock to the stripe wavelength, indicating that interaction-driven clustering organizes the intermediate-temperature landscape but is ultimately forestalled by stripe order at low temperature.