Forestalled Phase Separation as the Precursor to Stripe Order

Stripe order is a prominent feature in the phase diagram of the high-temperature cuprate superconductors. It has been confirmed as the lowest-energy state of the two-dimensional Fermi Hubbard model in certain parameter regimes. Upon increasing the temperature, stripes and the superconducting state give way to the enigmatic strange-metal and pseudogap regimes, whose precise nature remains a long-standing puzzle. Using modern tensor network techniques, we discover a crucial aspect of these regimes. Infinite projected entangled pair states (iPEPS) simulations in the fully two-dimensional limit reveal a maximum in the charge susceptibility at temperatures above the stripe order. This maximum is located around filling $n=0.9$ and intensifies upon cooling. Using minimally entangled typical thermal states (METTS) on finite cylinders, we attribute the enhanced charge susceptibility to the formation of charge clusters, reminiscent of phase separation where the system is partitioned into hole-rich and hole-depleted regions. In contrast to genuine phase separation, the charge cluster sizes fluctuate without a divergent charge susceptibility. Hence, while this precursor state features clustering of charge carriers, true phase separation is ultimately forestalled at lower temperatures by the onset of stripe order.