Two-particle States in One-dimensional Coupled Bose-Hubbard Models

We study doubly coupled Bose-Hubbard models and solve for the wave functions and energies of two-particle eigenstates. Even though the wave functions do not directly follow the form of a Bethe Ansatz, we describe an intuitive construction to express them as combinations of Choy-Haldane states for models with intra- and inter-species interaction. Our results show that the two-particle spectrum of the system comprises in general 4 different continua and 3 doublon dispersions with different interactions. Their energies vary with interaction strengths. The existence of doublons depends on the coupling strength between two species of bosons. We analyze one specific limit, i.e. with infinite interaction, and show the spectrum for all types of two-particle states and their spatial and entanglement properties.