Seminarium Fizyki Materii Skondensowanej

A central problem in cuprate physics is how superconductivity emerges from the spatially inhomogeneous normal state of a doped Mott insulator. We address this problem using finite-temperature tensor-network methods that access both thermodynamics and microscopic real-space structure. Using infinite projected entangled pair states, we find in the underdoped square-lattice Hubbard model a pronounced but finite maximum of the charge susceptibility near doping p~0.1, signalling strong incipient phase separation. Minimally entangled typical thermal states snapshots show that this regime is governed by fluctuating hole-rich clusters embedded in antiferromagnetic backgrounds. These clusters generate large low-momentum charge fluctuations, but instead of evolving into macroscopic segregation they are forestalled by the onset of stripe order at lower temperature. We then analyze the t⁣-t'⁣-J model and show that superconducting correlations are localized on these hole-rich clusters. At intermediate temperatures, pairing is fragmented across several localized singlet-pair modes associated with distinct hole clusters. As the temperature is lowered, these modes become increasingly aligned and extended, ultimately forming a coherent delocalized d-wave pattern. Additionally, finite-temperature spectral functions obtained from dynamical METTS connect the melting of stripes to the filling of the pseudogap. Our results identify fluctuating charge clusters as the finite-temperature precursor from which both stripe order and coherent superconductivity develop.