Effects of long-range inter-particle interactions and isolated defect on quantum walks of two hard-core bosons in one-dimensional lattices

Abstract

The quantum walks of two hard-core bosons in one-dimensional lattices under the effects of long-range inter-particle interactions are studied in detail. We also simulate the influence of an isolated defect that may exist in the lattice on the quantum walks of two particles by adding an additional potential energy on certain lattice site. Using exact diagonalization methods, the continuous-time quantum walks are directly simulated. The numerical simulations show that the range of interactions (long-range or short-range), the strength of the inter-particle interactions, the initial state of the two particles and the presence of the isolated defect have great influences on the quantum walks. Under the effect of strong long-range interactions, the particles initially located at non-adjacent lattice sites have a co-walking behavior, while under the short-range interactions (nearest-neighbor interactions) only two particles initially located at neighboring lattice sites can exhibit co-walking. When the isolated defect is introduced into the system with strong interactions, two particles initially on the same side of the isolated defect keep co-walking, while two particles initially located on either sides of the isolated defect or one particle located on the isolated defect keep stationary or walk near the defect, displaying the characteristics of localization. By using the second-order perturbation theory of degenerate quantum system, a comprehensive theoretical analysis of the above numerical results is given. The theoretical analysis reveals the underlying physical law of quantum walks of two particles in one-dimensional lattices under the effects of strong long-range interactions and isolated defect in the lattices.