Exotic localization for the two body bound states in the non-reciprocal Hubbard model

We investigate the localization behavior of two-body Hubbard model in the presence of non-reciprocal tunneling, where the interaction induced Anderson localization competes with the non-Hermitian skin effects and gives rise to diverse patterns of density profiles. Here, we present the non-Hermitian bound states obtained with the center of mass methods in the conditions of strong repulsive interaction, where a faded diagonal line localization is observed. While for the continuum limit, the non-Hermitian skin effects are manifested by non-zero windings of the eigen-energy spectrum. For the moderate interaction strength, it is illustrated that the system possesses multiple Lyapunov exponents due to the competence above and as a consequence, in sharp contrast to the corner localization, the two-body non-Hermitian continuum states can exhibit multiple localization center. By further including two-photon tunneling, topological nontrivial photon bound pairs can be obtained. Finally, the experimental simulations are proposed based on the platforms of the electrical circuit lattices.