Spectral functions of low-dimensional quantum systems

Dargel, Piet

dc.contributor.advisor	Pruschke, Thomas Prof. Dr.	de
dc.contributor.author	Dargel, Piet	de
dc.date.accessioned	2013-01-24T09:37:27Z	de
dc.date.available	2013-01-30T23:50:59Z	de
dc.date.issued	2013-01-24	de
dc.identifier.uri	http://hdl.handle.net/11858/00-1735-0000-000D-F1A3-6	de
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-3512
dc.language.iso	eng	de
dc.publisher	Niedersächsische Staats- und Universitätsbibliothek Göttingen	de
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subject.ddc	530	de
dc.title	Spectral functions of low-dimensional quantum systems	de
dc.type	doctoralThesis	de
dc.contributor.referee	Pruschke, Thomas Prof. Dr.	de
dc.date.examination	2012-11-30	de
dc.subject.gok	Physik (PPN621336750)	de
dc.description.abstracteng	The focus of this thesis is set on the calculation of spectral functions for low-dimensional quantum systems. At first the quantum many-body problem is introduced and the related spectral functions of interest are defined. In a next step the applied numerical algorithms are presented: Exact diagonalization & Lanczos algorithm, the numerical renormalization group (NRG) and the density matrix renormalization group (DMRG) in the formulation of matrix product states (MPS). The main focus is set on the calculation of spectral functions with these algorithms. In particular for the DMRG a new algorithm is presented which combines the Lanczos algorithm with matrix product states. The presented algorithms are applied to different problems. The first system denotes a copper crystal with magnetic (cobalt/iron) impurities. These materials are known Kondo-systems, i.e. they show an untypical increase in the resistivity with decreasing temperature. At low temperatures local moments will develop, which will be screened from the surrounding conduction band electrons. The ground state of the system is a long-range strongly correlated many-body state between conduction band electrons and local moments. In the singleparticle impurity spectral function a so-called Kondo resonance at the Fermi energy is formed below the Kondo temperature. In scanning tunneling microscope measurements the spectral function at the surface - the so-called local density of states - of the copper crystals with buried impurities in varying depth was measured. The goal of this study is to verify the existence of long-range Kondo signatures via a comparison of the spectral functions for impurities with different depth below the surface. Therefore in this work numerical simulations are used to calculate the local density of states at the surface. The single impurity Anderson model (SIAM) is applied which shows the Kondo resonance in the impurity spectral function. In order to calculate the local density of states at the surface of the copper crystal the equations of motion of the SIAM and the Dyson equation are used and then solved by a combination of numerical renormalization group and band structure calculations of the copper crystal (linear combination of atomic orbitals). The simulation for impurities in different depth below the surface and the experimental data are in very good agreement and hence support the measurement of a long-range Kondo signature. Furthermore the simulations allow to determine the Kondo temperature of a single impurity. The focus of the second part is set on the one-dimensional Heisenberg model. The spectral function of interest is here the dynamic spin structure factor. The newly developed MPS-Lanczos algorithm within the DMRG is used to calculate the dynamic spin structure factor. The results are compared to analytic results from the Bethe ansatz. In the end the new algorithm is discussed in respect to existing methods within the DMRG to calculate spectral functions.	de
dc.contributor.coReferee	Noack, Reinhard Prof.	de
dc.contributor.thirdReferee	Fehske, Holger Prof.	de
dc.subject.eng	Spectral function	de
dc.subject.eng	Kondo	de
dc.subject.eng	Density matrix renormalization group	de
dc.subject.eng	Numerical renormalization group	de
dc.subject.eng	solid state physics	de
dc.subject.eng	many-body problems	de
dc.subject.eng	computational physics	de
dc.subject.eng	impurity physics	de
dc.subject.eng	Heisenberg model	de
dc.subject.eng	condensed matter	de
dc.identifier.urn	urn:nbn:de:gbv:7-11858/00-1735-0000-000D-F1A3-6-8	de
dc.affiliation.institute	Fakultät für Physik	de
dc.identifier.ppn	737346175	de

Dateien

Name:Dissertation_Dargel_weboptimiert.pdf

Größe:4.401Mb

Format:PDF

Öffnen

Name:: Dissertation_Dargel_weboptimie ...
Größe:: 4.401Mb
Format:: PDF

Öffnen

Das Dokument erscheint in:

Fakultät für Physik (inkl. GAUSS) [925]

Zur Kurzanzeige