Spectral moment sum rules for the retarded Green’s function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

摘要

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retardednGreen’s function and for the zeroth and the first spectral moment sum rules for the retarded self-energy ofnthe inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemicalnpotential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We alsonevaluate these expressions for the homogeneous case in equilibrium, where all time dependence and externalnfields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sumnrules often depend on expectation values that cannot be determined simply from parameters in the Hamiltoniannlike the interaction strength and chemical potential but require knowledge of equal-time many-body expectationnvalues from some other source. We show how one can approximately evaluate these expectation values fornthe Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by theninteraction. We compare the exact moment relations to the calculated moments of spectral functions determinednfrom a variety of different numerical approximations and use them to benchmark their accuracy.