Title

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

Authors

Authors

J. K. Freericks; V. Turkowski; H. R. Krishnamurthy;M. Knap

Comments

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Abbreviated Journal Title

Phys. Rev. A

Keywords

INSULATOR TRANSITION; OPTICAL LATTICES; MOTT INSULATOR; SUPERFLUID; ATOMS; Optics; Physics, Atomic, Molecular & Chemical

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

Journal Title

Physical Review A

Volume

87

Issue/Number

1

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

12

WOS Identifier

WOS:000313939100009

ISSN

1050-2947

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