Quantum dynamics of Bose-Hubbard Hamiltonians beyond Hartree-Fock-Bogoliubov: The Bogoliubov backreaction approximation

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e formulate a method for studying the quantum field dynamics of ultracold Bose gases confined within optical lattice potentials, within the lowest Bloch-band Bose-Hubbard model. Our formalism extends the two-sites results of Phys. Rev. Lett. 86, 000568 (2001) to the general case of M lattice sites. The methodology is based on mapping the Bose-Hubbard Hamiltonian to an SU(M) pseudospin problem and truncating the resulting hierarchy of dynamical equations for correlation functions, up to pair-correlations between SU(M) generators. Agreement with few-site exact many-particle calculations is consistently better than the corresponding Hartree-Fock-Bogoliubov approximation. Moreover, our approximation compares favorably with a more elaborate two-particle irreducible effective action formalism, at a fraction of the analytic and numerical effort.