Topology and Bound States of Two Interacting Bosons in One-Dimensional Lattices

We present findings of nontrivial topological phases, edge states, bound states, and doublons for two interacting bosons in one-dimensional systems such as the Bose-Hubbard model, anyon-Hubbard model, and generalizations of the Su–Schrieffer–Heeger model. By mapping the N-body problem in a one-dimensional lattice into a one-body problem in N-dimensions we can use single-particle techniques to study the topology and few-body physics of identical interacting particles on one-dimensional tight-binding models. For two bosons on an infinite one-dimension chain, the configuration space is a semi-infinite square lattice that is periodic along the center of mass coordinates which enables us to study the system via Bloch's theorem. Except for defects on its edge given by two-particle interactions, the semi-infinite unit cell is periodic in the relative distance of the two particles. Without losing information about the two-body physics, we can truncate at a large relative distance where configurations correspond to essentially free particles. The effective Hamiltonian of our system can now be written as a one-dimensional Bloch Hamiltonian, allowing us to apply well known tools from single-particle band theory. We use these methods to identify new types of two-body bound states in one-dimensional tight-binding models.