Non-Hermitian delocalization of interacting directed polymers on periodic substrates

Non-Hermitian Hamiltonians describe the dynamics of systems experiencing energy flow, gain, and loss in a variety of physical settings. When combined with periodic potentials, non-Hermiticity brings new twists to band-based phenomena such as topological modes and metal-insulator transitions. We explore the interplay of band theory and non-Hermitian mechanics in a classical system of interacting directed polymers on a substrate with periodic grooves. At thermal equilibrium, the density profiles of the polymers map onto the quantum statistics of fermions experiencing a constant imaginary vector potential in addition to the (real) periodic substrate potential. The strength of the vector potential, which renders the problem non-Hermitian, is controlled by a transverse shear force applied to the polymer ends. By ramping up the shear, we drive a transition from a localized band-insulator state with each polymer aligned to a unique groove, to a tilted configuration in which polymers are delocalized across many grooves. Besides advancing known mechanisms of delocalization in directed polymers, our results provide a purely classical manifestation of non-Hermitian band physics enabled by thermal fluctuations and interactions.