Sum-rules and bath-parametrization for quantum cluster theories

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dc.creatorKoch, Erik
dc.creatorSangiovanni, Giorgio
dc.creatorGunnarsson, Olle
dc.date2008-04-21
dc.date.accessioned2026-07-07T09:59:51Z
dc.date.available2026-07-07T09:59:51Z
dc.descriptionWe analyze cellular dynamical mean-field theory (CDMFT) and the dynamical cluster approximation (DCA). We derive exact sum-rules for the hybridization functions and give examples for DMFT, CDMFT, and DCA. For impurity solvers based on a Hamiltonian, these sum-rules can be used to monitor convergence of the bath-parametrization. We further discuss how the symmetry of the cluster naturally leads to a decomposition of the bath Green matrix into irreducible components, which can be parametrized independently, and give an explicit recipe for finding the optimal bath-parametrization. As a benchmark we revisit the one-dimensional Hubbard model. We carefully analyze the evolution of the density as a function of chemical potential and find that, close to the Mott transition, convergence with cluster size is unexpectedly slow. In two dimensions we find, that we need so many bath-sites to obtain a reliable parametrization that Lanczos calculations are hardly feasible with current computers. For such large baths our symmetry-adapted approach should prove crucial for finding a reliable bath-parametrization.
dc.description11 pages, 14 figures
dc.identifierhttps://arxiv.org/abs/0804.3320
dc.identifierhttp://arxiv.org/abs/0804.3320
dc.identifierPhys. Rev. B 78, 115102 (2008)
dc.identifierdoi:10.1103/PhysRevB.78.115102
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168175
dc.subjectStrongly Correlated Electrons
dc.titleSum-rules and bath-parametrization for quantum cluster theories
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