Reservoir-conditioned virtual returns generate random Liouvillian skin localization in a reciprocal Mott insulator

Abstract

Directional dissipation can concentrate relaxation modes in space, but connecting this accumulation to controlled microscopic processes in correlated matter requires separating virtual charge motion from spin coherence. We study this connection in a half-filled Hubbard chain with reciprocal hopping and number-conserving, direction-selective returns of virtual doublon--hole defects. Eliminating charge defects and then Mott coherences yields asymmetric spin-exchange rates under an explicit separation of timescales, with full short-chain dynamics supporting the reduction on finite exchange times. Balanced random returns concentrate the stationary population and several low-lying right modes at sample-selected positions rather than a predetermined edge, producing random Liouvillian skin localization despite zero end-to-end logarithmic rate bias. The accumulated rate imbalance determines an exact finite-density hard-core stationary state and a one-particle activated relaxation scale governed by random barriers. This connection between locally calibrated return rates, many-body stationary weights and slow relaxation offers a means of controlling transport in constrained open quantum matter without changing the reciprocal Hamiltonian.