Gaussian time-dependent variational principle for the Bose-Hubbard model

摘要: We systematically extend Bogoliubov theory beyond the mean-field approximation of Bose-Hubbard model in superfluid phase. Our approach is based on time-dependent variational principle applied to family all Gaussian states (i.e., TDVP). First, we find best ground-state within our class using imaginary time evolution 1D, 2D, and 3D. benchmark results by comparing DMRG 1D. Second, compute approximate one- two-particle excitation spectrum as eigenvalues linearized projected equations motion (linearized gapless Goldstone mode, a continuum excitations doublon mode. discuss relation gap between mode energy Higgs Third, linear response functions for perturbations describing density variation lattice modulation their relations experiment. methods can be any that are or quadratic creation/annihilation operators. Finally, provide comprehensive overview how related well-known methods, such traditional random phase approximation.