Coupled-cluster theory for bosons in rings and optical lattices

Bosons in optical lattices and rings are attractive and active fields of research in cold-atom physics. Here, we apply our recently developed coupled-cluster approach for bosons in external traps to these systems, and extend it to the lowest-in-energy excited states with total quasi- or angular-momentum k. In the coupled-cluster approach the exact many-boson ground state is obtained by applying an exponential operator exp{T}, T = ∑_{n = 1}^N T_n to the ground configuration, which is (usually) the state where the bosons occupy a single orbital. For excited states, a second exponential operator exp{T^(k)}, T^(k) = ∑_{n = 1}^N T_n^(k) is employed to accommodate the remaining excitations from the unperturbed excited configuration. Due to the conservation of momentum, T₁ and T₁^(k) can vanish. Working equations for coupled-cluster (singles) doubles (CCD) are provided and their implications are briefly discussed.