Cellular Dynamical Mean-field Theory in large Impurity Clusters

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dc.contributor.advisor Andergassen, Sabine (Prof. Dr.)
dc.contributor.author Klett, Marcel
dc.date.accessioned 2020-12-29T09:27:22Z
dc.date.available 2020-12-29T09:27:22Z
dc.date.issued 2021-10-20
dc.identifier.uri http://hdl.handle.net/10900/110978
dc.identifier.uri http://nbn-resolving.de/urn:nbn:de:bsz:21-dspace-1109782 de_DE
dc.identifier.uri http://dx.doi.org/10.15496/publikation-52354
dc.description.abstract Even after decades of intense research, the single band Hubbard model representing the fundamental model for interacting quantum systems and electronic correlations remains an unsolved cornerstone paradigm in theoretical solid state physics. Within the non-perturbative dynamical mean-field theory (DMFT), the lattice problem is mapped to a self-consistent auxiliary quantum impurity model leading to a local approximation of the self-energy. Nonlocal correlations can be included by the real-space cluster extension of the DMFT (CDMFT). Enlarging the unit cell makes the calculation of a numerically exact solution in CDMFT very challenging. We here use a quantum Monte-Carlo approach in the imaginary-time space in order to solve the self-consistency equations for different cluster sizes. In order to restore the broken translational symmetry re-periodization schemes for the Green function, the self-energy, or its cumulants have been introduced. However, these suffer from ambiguity and may even lead to convergence problems when attempted inside the self-consistency loop. The comparison to numerically exact diagrammatic quantum Monte Carlo calculations shows that introducing a so-called centerfocused extrapolation (CFE) to approximate the lattice self-energy yields very accurate results. Moreover, the CFE converges faster with the cluster size than previous periodization schemes. We here perform a detailed CDMFT analysis for the single-band Hubbard model on the 2D square lattice, reaching real-space cluster sizes of up to 9x9 sites. In addition to spectral properties, we also compute two-particle correlation functions which are not accessible in DMFT. Using benchmarks against diagrammatic Monte Carlo at high temperature, we show that the cluster spin susceptibility can be extrapolated to the exact result at large cluster size. In particular, the exponential decay of spin-spin correlations is very well captured by CDMFT calculations, even when correlations extend beyond the size of the cluster. We further present results at lower temperature T and larger $U$ than the range currently accessible with diagrammatic Monte Carlo methods techniques. The CDMFT+CFE represents therefore a powerful computational tool to access the physics of non-local correlations beyond dynamical mean-field theory. en
dc.language.iso en de_DE
dc.publisher Universität Tübingen de_DE
dc.rights ubt-podok de_DE
dc.rights.uri http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=de de_DE
dc.rights.uri http://tobias-lib.uni-tuebingen.de/doku/lic_mit_pod.php?la=en en
dc.subject.classification Dynamische Molekularfeldtheorie , Kondensierte Materie de_DE
dc.subject.ddc 530 de_DE
dc.subject.other CDMFT en
dc.subject.other DMFT en
dc.subject.other Dynamical mean-field theory en
dc.subject.other Cellular dynamical mean-field theory en
dc.title Cellular Dynamical Mean-field Theory in large Impurity Clusters en
dc.type Dissertation de_DE
dcterms.dateAccepted 2020-10-20
utue.publikation.fachbereich Physik de_DE
utue.publikation.fakultaet 7 Mathematisch-Naturwissenschaftliche Fakultät de_DE
utue.publikation.noppn yes de_DE

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