Interaction-Induced Breakdown of Anderson Localization: Thermodynamic Segregation disguised as the Skin Effect

Abstract: We investigate the interplay between strong disorder and repulsive interactions in the one-dimensional Fermi-Hubbard model under open boundary conditions. While uncorrelated disorder is widely accepted to localize all single-particle eigenstates, a phenomenon typically reinforced by interactions in the Many-Body Localization (MBL) regime, we report a counter-intuitive breakdown of this paradigm. We demonstrate that strong repulsive interactions can overcome disorder-induced localization, driving the system into a macroscopically segregated phase where spin species accumulate at opposite boundaries. Although this boundary accumulation phenomenologically mimics the Non-Hermitian Skin Effect (NHSE) observed in non-reciprocal systems, our comprehensive analysis reveals a fundamentally different origin. By performing a rigorous control experiment in the Hermitian limit, we prove that the segregation persists without non-reciprocity, identifying many-body energy minimization as the primary driver. This "interaction-induced segregation" manifests as a sharp thermodynamic crossover, characterized by a divergent energy susceptibility, challenging the conventional understanding of disorder-interaction competition in open quantum systems.