State-selective entanglement and point-gap topology in the unidirectional Bose-Hubbard chain

We study the effect of repulsive interactions on skin modes and entanglement in the unidirectional Bose--Hubbard model. Although the ground state of this integrable model undergoes a superfluid--Mott transition with suppressed skin accumulation, the corresponding change in entanglement depends on the selected many-body state. We compare the ground state with the steady state, defined as the largest-imaginary-energy eigenstate in the zero-momentum sector. For sixteen sites at unit filling, we find that the ground-state density approaches uniform filling and its entanglement decreases toward the Mott limit, whereas the steady states exhibit a nonmonotonic entanglement crossover. At intermediate interaction (U/t=10), the second Rényi entropy of the steady state develops four spatial maxima. We show that these maxima are accounted for by competing subsystem-number sectors within a dominant configuration manifold of four doublons and four holons, but not by the subsystem particle-number variance alone. The dominant global onsite-pair manifold retains the same entropy peak structure. At strong interaction, projection onto the one-doublon--one-holon manifold closely reproduces the full entropy profile and its two edge peaks. Furthermore, we demonstrate that the many-body winding about the origin remains nonzero at strong interaction; an exact two-site example shows how it becomes ill-defined in the singular projected U/t to infinity limit. Our results distinguish ground-state skin suppression from state-selective entanglement and point-gap topology.