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

Freericks, JK and Turkowski, V and Krishnamurthy, HR and Knap, M (2013) Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium. In: PHYSICAL REVIEW A, 87 (1).

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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

Item Type:	Journal Article
Publication:	PHYSICAL REVIEW A
Publisher:	AMER PHYSICAL SOC
Additional Information:	Copyright for this article belongs to AMER PHYSICAL SOC,USA
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	22 Feb 2013 09:31
Last Modified:	22 Feb 2013 09:31
URI:	http://eprints.iisc.ac.in/id/eprint/45846

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