Properties of the single-site reduced density matrix in the Bose-Bose resonance model in the ground state and in quantum quenches

We study properties of the single-site reduced density matrix in the Bose-Bose resonance model as a function of system parameters. This model describes a single-component Bose gas with a resonant coupling to a diatomic molecular state, here defined on a lattice. A main goal is to demonstrate that the eigenstates of the single-site reduced density matrix have structures that are characteristic for the various quantum phases of this system. Since the Hamiltonian conserves only the global particle number but not the number of bosons and molecules individually, these eigenstates, referred to as optimal modes, can be nontrivial linear combinations of bare eigenstates of the molecular and boson particle number. We numerically analyze the optimal modes and their weights, the latter giving the importance of the corresponding state, in the ground state of the Bose-Bose resonance model. We find that the single-site von Neumann entropy is sensitive to the location of the phase boundaries. We explain the structure of the optimal modes and their weight spectra using perturbation theory and via a comparison to results for the single-component Bose-Hubbard model. We further study the dynamical evolution of the optimal modes and of the single-site entanglement entropy in two quantum quenches that cross phase boundaries of the model and show that these quantities are thermal in the steady state. For our numerical calculations, we use the density matrix renormalization group method for ground-state calculations and time evolution in a Krylov subspace for the quench dynamics as well as exact diagonalization.