Solution of the Bose-Hubbard model using doorway states

– We introduce an efficient method to solve the Bose-Hubbard model. The Schrödinger equation is solved by the successive construction of doorway states. The ground state wavefunction derived by this method contains all relevant many-body correlations introduced by the hamiltonian, but the dimensionality of the Hilbert space is greatly reduced. We apply the doorway method to obtain the chemical potential, the on-site fluctuations and the visibility of the interference pattern arising from atoms in a one-dimensional periodic lattice. Excellent qualitative agreement with exact numerical calculations as well as recent experimental observations is found. The physics of strongly interacting quantum systems has been subject of intense investigations since the early days of quantum mechanics. With the recent developments in the field of ultracold quantum gases, systems of strongly correlated bosonic and fermionic atoms with tunable interactions have become amendable to experimental studies [1–5]. Complete theoretical understanding of these coupled many-body systems is difficult, and only rare examples exist, for which analytical solutions for the ground state could be explicitly been given [6]. The description generally has to rely upon approximation methods such as the density-grouprenormalization [7], a Gutzwiller ansatz [8–10] and quantum Monte Carlo approaches [11]. Of particular importance is the Bose-Hubbard model, which serves as a prototype system exhibiting a quantum phase transition [12]. Triggered by the recent observation of this phase transition from a superfluid to a Mott-insulating phase with bosonic atoms in one(1D) and three-dimensional (3D) optical lattices [3, 4, 13], the ground state and correlation properties of the Bose-Hubbard model have been extensively investigated by a large number of groups [14–16]. In this Letter, we explore an alternative and particularly efficient theoretical approach to solve the Bose-Hubbard model. The method is based on the construction of doorway projectors as initially introduced by Feshbach in the context of nuclear scattering [17]. A similar approach appears in some other areas of physics under different names. For example, in