arXiv:1011.6019

Vertex coupling in quantum graphs: approximations by scaled Schroedinger operators

Pavel Exner

Published Nov 28, 2010• 4 citations

Abstract

We review recent progress in understanding the physical meaning of quantum graph models through analysis of their vertex coupling approximations.

DOI: 10.48550/arxiv.1011.6019

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arXiv:1011.6019

Vertex coupling in quantum graphs: approximations by scaled Schroedinger operators

Pavel Exner

Published Nov 28, 2010• 4 citations

arXiv HTML PDF

Abstract

We review recent progress in understanding the physical meaning of quantum graph models through analysis of their vertex coupling approximations.

DOI: 10.48550/arxiv.1011.6019

Related papers

VERTEX COUPLINGS IN QUANTUM GRAPHS: APPROXIMATIONS BY SCALED SCHRÖDINGER OPERATORS

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We review recent progress in understanding the physical meaning of quantum graph models through analysis of their vertex coupling approximations.

Mathematics in Science and TechnologyJun 1, 20117 citations

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Dynamical vertex approximation -- an introduction

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We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D $Γ$ A). This approach contains the important local correlations of DMFT, giving, among others, rise to quasiparticle renormalizations, Mott-Hubbard transitions and magnetism, but also non-local correlations beyond. The latter are at the very essence of many physical phenomena in strongly correlated elecectron systems. As correlations are treated equally on all length scales, D $Γ$ A allows us to describe physical phenomena such as magnons, quantum criticality, and the interplay between antiferromagnetism and superconductivity. We review results hitherto obtained for the Hubbard model in dimensions d=3, 2, and 1.We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D$Γ$A). This approach contains the important local correlations of DMFT, giving, among others, rise to quasiparticle renormalizations, Mott-Hubbard transitions and magnetism, but also non-local correlations beyond. The latter are at the very essence of many physical phenomena in strongly correlated elecectron systems. As correlations are treated equally on all length scales, D$Γ$A allows us to describe physical phenomena such as magnons, quantum criticality, and the interplay between antiferromagnetism and superconductivity. We review results hitherto obtained for the Hubbard model in dimensions d=3, 2, and 1.

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A. A. Lavrukhine, A. I. Popov, I. Yu. Popov

Indian Journal of PhysicsJan 4, 20230 citations

We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D

Γ

A). This approach contains the important local correlations of DMFT, giving, among others, rise to quasiparticle renormalizations, Mott-Hubbard transitions and magnetism, but also non-local correlations beyond. The latter are at the very essence of many physical phenomena in strongly correlated elecectron systems. As correlations are treated equally on all length scales, D

Γ

A allows us to describe physical phenomena such as magnons, quantum criticality, and the interplay between antiferromagnetism and superconductivity. We review results hitherto obtained for the Hubbard model in dimensions d=3, 2, and 1.