Flat bands arising from destructive interference are qualified candidates for hosting exotic states of matter. Here we investigate the spectral and localization features of two interacting particles in a non-Hermitian flat-band lattice, described by a flux-dressed rhombic-Hubbard model with nonreciprocal hoppings, and unravel some intriguing results. In the noninteracting scenario, the flat bands survive under nonreciprocity, and we identify the emergence of two-particle hybridized flat-band states formed by the bonding of a single-particle skin-edge state and a localized flat-band state. Upon strong interactions, we uncover the transition from flat-band localization to skin localization and the emergence of doublon edge states. Remarkably, unlike the interaction-induced flat-band localization in Hermitian cases, we find that the interaction leads to all-dispersive-skin bands for $\pi /2$ flux. A perturbation theory incorporating forth-order processes is developed to understand these results. Finally, we propose a feasible experimental scheme by emulating the two-particle Hilbert space using electric circuits. Our work offers insights into the emergent correlated states in non-Hermitian systems and expands our understanding of non-Hermitian many-body physics.

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• Doublon
• Flat bands
• Localization
• Skin effect
• Non-Hermitian systems