@article{ISI:000313939100009,
 abstract = {We derive exact expressions for the zeroth and the first three spectral
moment sum rules for the retarded Green's function and for the zeroth
and the first spectral moment sum rules for the retarded self-energy of
the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local
on-site repulsion and the chemical potential are time-dependent, and in
the presence of an external time-dependent electromagnetic field. We
also evaluate these expressions for the homogeneous case in equilibrium,
where all time dependence and external fields vanish. Unlike similar sum
rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the
sum rules often depend on expectation values that cannot be determined
simply from parameters in the Hamiltonian like the interaction strength
and chemical potential but require knowledge of equal-time many-body
expectation values from some other source. We show how one can
approximately evaluate these expectation values for the Mott-insulating
phase in a systematic strong-coupling expansion in powers of the hopping
divided by the interaction. We compare the exact moment relations to the
calculated moments of spectral functions determined from a variety of
different numerical approximations and use them to benchmark their
accuracy. DOI: 10.1103/PhysRevA.87.013628},
 article-number = {013628},
 author = {Freericks, J. K. and Turkowski, V. and Krishnamurthy, H. R. and Knap, M.},
 doi = {10.1103/PhysRevA.87.013628},
 eissn = {1094-1622},
 issn = {1050-2947},
 journal = {PHYSICAL REVIEW A},
 month = {JAN 24},
 number = {1},
 orcid-numbers = {Knap, Michael/0000-0002-7093-9502
Freericks, James K/0000-0002-6232-9165},
 researcherid-numbers = {Knap, Michael/H-3344-2011
Freericks, James K/D-7502-2011},
 times-cited = {2},
 title = {Spectral moment sum rules for the retarded Green's function and
self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and
nonequilibrium},
 unique-id = {ISI:000313939100009},
 volume = {87},
 year = {2013}
}