Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice

In this work, we analyze the single-particle Green function of the Hubbard model on the Bethe lattice with an infinite number of nearest neighbors at zero temperature. The Hubbard model is conceptually the simplest many-electron model. Nevertheless, it poses a most difficult many-body problem. Exce...

Ausführliche Beschreibung

Gespeichert in:
1. Verfasser: Ruhl, Daniel F.
Beteiligte: Gebhard, Florian (Prof. Dr.) (BetreuerIn (Doktorarbeit))
Format: Dissertation
Sprache:Englisch
Veröffentlicht: Philipps-Universität Marburg 2010
Physik
Schlagworte:
Online Zugang:PDF-Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
publishDate 2010
era_facet 2010
topic Single Impurity Anderson Model
Correlated Electrons
Physik
Störungstheorie
Hubbard-Modell
Anderson-Modell
Hubbard Model
Mehrpunktfunktion
Dynamical Mean Field Theory
Mott-Transition
Selbstkonsistenz
Mott-Übergang
spellingShingle Single Impurity Anderson Model
Correlated Electrons
Physik
Störungstheorie
Hubbard-Modell
Anderson-Modell
Hubbard Model
Mehrpunktfunktion
Dynamical Mean Field Theory
Mott-Transition
Selbstkonsistenz
Mott-Übergang
Ruhl, Daniel F.
In dieser Arbeit beschäftigen wir uns mit der theoretischen Beschreibung des korrelierten Mott-Hubbard Isolators. Obwohl das Hubbard Modell das konzeptionell einfachste Modell korrelierter Elektronen darstellt, wurde bisher nur in einer Dimension eine exakte Lösung gefunden. Auch das Modell in unendlichen Dimensionen ist bisher nicht exakt gelöst. Zielsetzung unserer Arbeit ist die analytische Berechnung der Einteilchen-Zustandsdichte sowie der Lücke für Ladungsanregungen des Mott-Hubbard Isolators in unendlichen Dimensionen. Hierzu berechnen wir die lokale Greenfunktion des Hubbard Modells auf dem Bethegitter mit unendlich vielen nächsten Nachbarn bei der Temperatur T = 0. Unser Startpunkt ist die Dynamische Molekularfeldtheorie (DMFT), in der das auf dem Gitter definierte Hubbard Modell auf das Single Impurity Anderson Model (SIAM) abgebildet wird. Mit Hilfe der von uns auf das vorliegende Problem angepaßten Kato-Takahashi Störungstheorie, sind wir in der Lage die Lösungen der Selbstkonsistenzgleichungen der DMFT bis zur dritten Ordnung in 1/U anzugeben. Hiermit präsentieren wir zum ersten Mal eine analytische Lösung der Selbstkonsistenzgleichungen der DMFT für den Mott-Hubbard Isolator.
Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice
institution Physik
publisher Philipps-Universität Marburg
oai_set_str_mv ddc:530
open_access
doc-type:doctoralThesis
xMetaDissPlus
dewey-raw 530
dewey-search 530
genre Physics
genre_facet Physics
topic_facet Physik
author Ruhl, Daniel F.
last_indexed 2011-08-10T23:59:59Z
language English
first_indexed 2010-07-08T00:00:00Z
contents In dieser Arbeit beschäftigen wir uns mit der theoretischen Beschreibung des korrelierten Mott-Hubbard Isolators. Obwohl das Hubbard Modell das konzeptionell einfachste Modell korrelierter Elektronen darstellt, wurde bisher nur in einer Dimension eine exakte Lösung gefunden. Auch das Modell in unendlichen Dimensionen ist bisher nicht exakt gelöst. Zielsetzung unserer Arbeit ist die analytische Berechnung der Einteilchen-Zustandsdichte sowie der Lücke für Ladungsanregungen des Mott-Hubbard Isolators in unendlichen Dimensionen. Hierzu berechnen wir die lokale Greenfunktion des Hubbard Modells auf dem Bethegitter mit unendlich vielen nächsten Nachbarn bei der Temperatur T = 0. Unser Startpunkt ist die Dynamische Molekularfeldtheorie (DMFT), in der das auf dem Gitter definierte Hubbard Modell auf das Single Impurity Anderson Model (SIAM) abgebildet wird. Mit Hilfe der von uns auf das vorliegende Problem angepaßten Kato-Takahashi Störungstheorie, sind wir in der Lage die Lösungen der Selbstkonsistenzgleichungen der DMFT bis zur dritten Ordnung in 1/U anzugeben. Hiermit präsentieren wir zum ersten Mal eine analytische Lösung der Selbstkonsistenzgleichungen der DMFT für den Mott-Hubbard Isolator.
description In this work, we analyze the single-particle Green function of the Hubbard model on the Bethe lattice with an infinite number of nearest neighbors at zero temperature. The Hubbard model is conceptually the simplest many-electron model. Nevertheless, it poses a most difficult many-body problem. Except in one spatial dimension, no exact solution has been found up to today. Therefore, systematic analytical approximations are of major importance as they provide results in the thermodynamic limit against which numerical methods can be tested. We aim to calculate the single-particle density of states and the gap for charge-carrying single-particle excitations. Both of these quantities are rather difficult to obtain in numerical studies which necessarily deal with rather small system sizes. Reliable analytical results provide reliable benchmark tests for the numerics. We employ the Dynamical Mean-Field theory (DMFT), which permits the mapping of the Hubbard model in infinite dimensions or, equivalently, with an infinite number of nearest neighbors, onto an effective quantum impurity system. We use the Single Impurity Anderson Model (SIAM) as the quantum impurity model. New to our approach is the fact that we solve the DMFT equations for the Mott-Hubbard insulator up to third order in 1/U . We achieve this goal with the help of the Kato-Takahashi perturbation after successfully adapting it to our problem. This is the first time an analytical solution of the DMFT self-consistency equations for the insulator has been found.
author2 Gebhard, Florian (Prof. Dr.)
author2_role ths
title_alt Lösung der Selbstkonsistenzgleichungen der Dynamischen Molekularfeldtheorie für den Mott-Hubbard Isolator auf einem Bethegitter bei starker Kopplung
url http://archiv.ub.uni-marburg.de/diss/z2010/0377/pdf/ddfr.pdf
building Fachbereich Physik
license_str http://archiv.ub.uni-marburg.de/adm/urhg.html
title Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice
title_short Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice
title_full Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice
title_fullStr Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice
title_full_unstemmed Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice
title_sort Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice
ref_str_mv references
format Dissertation
thumbnail http://archiv.ub.uni-marburg.de/diss/z2010/0377/cover.png
spelling diss/z2010/0377 2010 2011-08-10 2010-07-08 In dieser Arbeit beschäftigen wir uns mit der theoretischen Beschreibung des korrelierten Mott-Hubbard Isolators. Obwohl das Hubbard Modell das konzeptionell einfachste Modell korrelierter Elektronen darstellt, wurde bisher nur in einer Dimension eine exakte Lösung gefunden. Auch das Modell in unendlichen Dimensionen ist bisher nicht exakt gelöst. Zielsetzung unserer Arbeit ist die analytische Berechnung der Einteilchen-Zustandsdichte sowie der Lücke für Ladungsanregungen des Mott-Hubbard Isolators in unendlichen Dimensionen. Hierzu berechnen wir die lokale Greenfunktion des Hubbard Modells auf dem Bethegitter mit unendlich vielen nächsten Nachbarn bei der Temperatur T = 0. Unser Startpunkt ist die Dynamische Molekularfeldtheorie (DMFT), in der das auf dem Gitter definierte Hubbard Modell auf das Single Impurity Anderson Model (SIAM) abgebildet wird. Mit Hilfe der von uns auf das vorliegende Problem angepaßten Kato-Takahashi Störungstheorie, sind wir in der Lage die Lösungen der Selbstkonsistenzgleichungen der DMFT bis zur dritten Ordnung in 1/U anzugeben. Hiermit präsentieren wir zum ersten Mal eine analytische Lösung der Selbstkonsistenzgleichungen der DMFT für den Mott-Hubbard Isolator. In this work, we analyze the single-particle Green function of the Hubbard model on the Bethe lattice with an infinite number of nearest neighbors at zero temperature. The Hubbard model is conceptually the simplest many-electron model. Nevertheless, it poses a most difficult many-body problem. Except in one spatial dimension, no exact solution has been found up to today. Therefore, systematic analytical approximations are of major importance as they provide results in the thermodynamic limit against which numerical methods can be tested. We aim to calculate the single-particle density of states and the gap for charge-carrying single-particle excitations. Both of these quantities are rather difficult to obtain in numerical studies which necessarily deal with rather small system sizes. Reliable analytical results provide reliable benchmark tests for the numerics. We employ the Dynamical Mean-Field theory (DMFT), which permits the mapping of the Hubbard model in infinite dimensions or, equivalently, with an infinite number of nearest neighbors, onto an effective quantum impurity system. We use the Single Impurity Anderson Model (SIAM) as the quantum impurity model. New to our approach is the fact that we solve the DMFT equations for the Mott-Hubbard insulator up to third order in 1/U . We achieve this goal with the help of the Kato-Takahashi perturbation after successfully adapting it to our problem. This is the first time an analytical solution of the DMFT self-consistency equations for the insulator has been found. Lösung der Selbstkonsistenzgleichungen der Dynamischen Molekularfeldtheorie für den Mott-Hubbard Isolator auf einem Bethegitter bei starker Kopplung 2010-06-22 Strong-Coupling Solution of the Dynamical Mean-Field Equations for the Mott-Hubbard Insulator on a Bethe Lattice J. Bardeen, L. N. Cooper, and J. R. Schrieffer, " Microscopic theory of superconductivity " , Physical Review, vol. 106, pp. 162–164, 1957. 1957 Microscopic theory of superconductivity E. Wigner and F. Seitz, " On the constitution of metallic sodium " , Physical Review, vol. 43, pp. 804–810, 1933. 1933 On the constitution of metallic sodium E. Kalinowski and F. Gebhard, " Mott-Hubbard insulator in infinite dimensions " , Journal of Low Temperature Physics, vol. 126, pp. 979–1007, 2002. 2002 Mott-Hubbard insulator in infinite dimensions M. P. Eastwood, F. Gebhard, E. Kalinowski, S. Nishimoto, and R. M. Noack, " Analytical and numerical treatment of the Mott-Hubbard insulator in infinite dimensions " , The European Physical Journal B, vol. 35, pp. 155–175, 2003. 2003 Analytical and numerical treatment of the Mott-Hubbard insulator in infinite dimensions M. Eckstein, M. Kollar, K. Byczuk, and D. Vollhardt, " Hopping on the Bethe lattice: Exact results for densities of states and Dynamical Mean-Field Theory " , Physical Review B, vol. 71, p. 235119, 2005. 2005 Hopping on the Bethe lattice: Exact results for densities of states and Dynamical Mean-Field Theory R. Bulla, T. A. Costi, and T. Pruschke, " Numerical renormalization group method for quantum impurity systems " , Reviews of Modern Physics, vol. 80, pp. 395–450, 2008. 2008 Numerical renormalization group method for quantum impurity systems F. H. L. Essler, V. E. Korepin, and K. Schoutens, " Complete solution of the one-dimensional Hubbard model " , Physical Review Letters, vol. 67, pp. 3848–3851, 1991. 1991 Complete solution of the one-dimensional Hubbard model T. Hanisch, B. Kleine, and E. Müller-Hartmann, " Ferromagnetism in the Hubbard model: in- stability of the Nagaoka state on the triangular, honeycomb and kagome lattices " , Annalen der Physik, vol. 507, no. 4, pp. 303–328, 1995. 1995 Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular, honeycomb and kagome lattices U. Fano, " Effects of configuration interaction on intensities and phase shifts " , Physical Review, vol. 124, pp. 1866–1878, 1961. 1961 Effects of configuration interaction on intensities and phase shifts M. Nahrgang, " Multichain Approach to the Single-Impurity Anderson Model in the Dynamical Mean-Field Theory " , Diplomarbeit, Philipps-Universität Marburg, 2008. 2008 Multichain Approach to the Single-Impurity Anderson Model in the Dynamical Mean-Field Theory P. de Faget de Casteljau and J. Friedel, " ´ Etude de la résistivité et du pouvoir thermoélectrique des impuretés dissoutes dans les métaux nobles " , Journal de Physique et Le Radium, vol. 17, no. 1, pp. 27–32, 1956. 1956 ´ Etude de la résistivité et du pouvoir thermoélectrique des impuretés dissoutes dans les métaux nobles J. Friedel, " Sur la structuré electronique des métaux et alliages de transition et des métaux lourds " , Journal de Physique et Le Radium, vol. 19, no. 6, pp. 573–581, 1958. 1958 Sur la structuré electronique des métaux et alliages de transition et des métaux lourds P. Weiss, " L'hypothèse du champ moléculaire et la propriété ferromagnétique " , Journal de Physique Théorique et Appliquée, vol. 6, no. 1, pp. 661–690, 1907. 1907 L'hypothèse du champ moléculaire et la propriété ferromagnétique M.-B. Lepetit, M. Cousy, and G. Pastor, " Density-matrix renormalization study of the Hubbard model on a Bethe lattice " , European Physical Journal B, vol. 13, no. 3, pp. 421–427, 2000. 2000 Density-matrix renormalization study of the Hubbard model on a Bethe lattice L. Kantorovich, Quantum Theory of the Solid State: An Introduction, vol. 136 of Fundamental Theories of Physics. Kluwer Academic Publishers, 2004. 2004 Quantum Theory of the Solid State: An Introduction of Fundamental Theories of Physics E. H. Lieb and F. Y. Wu, " Absence of Mott transition in an exact solution of the short-range, one-band model in one dimension " , Physical Review Letters, vol. 20, pp. 1445–1448, 1968. 1968 Absence of Mott transition in an exact solution of the short-range, one-band model in one dimension P. Phillips, Advanced Solid State Physics. Advanced Book Program, Westview Press, 2003. 2003 Advanced Solid State Physics Advanced Book Program R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem. Dover Publications Inc., second ed., 1992. 1992 A Guide to Feynman Diagrams in the Many-Body Problem J. D. Cloizeaux, " Analytical properties of n-dimensional energy bands and Wannier functions " , Physical Review, vol. 135, pp. A698–A707, 1964. 1964 Analytical properties of n-dimensional energy bands and Wannier functions W. Kohn, " Analytic properties of Bloch waves and Wannier functions " , Physical Review, vol. 115, pp. 809–821, 1959. 1959 Analytic properties of Bloch waves and Wannier functions C. Lanczos, " An iteration method for the solution of the eigenvalue problem of linear differential and integral operators " , Journal of Research of the National Bureau of Standards, vol. 45, pp. 255– 282, 1950. 1950 An iteration method for the solution of the eigenvalue problem of linear differential and integral operators P. L. Taylor and O. Heinonen, A Quantum Approach to Condensed Matter Physics. Cambridge University Press, 2002. Bibliography [20] G. Czycholl, Theoretische Festkörperphysik. Springer, 2004. 2002 A Quantum Approach to Condensed Matter Physics R. Abou-Chacra, D. J. Thouless, and P. W. Anderson, " A selfconsistent theory of localization " , Journal of Physics C: Solid State Physics, vol. 6, no. 10, pp. 1734–1752, 1973. Bibliography [59] R. Abou-Chacra and D. J. Thouless, " Self-consistent theory of localization: II. Localization near the band edges " , Journal of Physics C: Solid State Physics, vol. 7, no. 1, pp. 65–75, 1974. 1973 A selfconsistent theory of localization Self-consistent theory of localization: II. Localization near the band edges E. Ising, " Beitrag zur Theorie des Ferromagnetismus " , Zeitschrift für Physik, vol. 31, pp. 253–258, 1925. 1925 Beitrag zur Theorie des Ferromagnetismus J. Chalupa, P. L. Leath, and G. R. Reich, " Bootstrap percolation on a Bethe lattice " , Journal of Physics C: Solid State Physics, vol. 12, no. 1, pp. L31–L35, 1979. 1979 Bootstrap percolation on a Bethe lattice L. N. Cooper, " Bound electron pairs in a degenerate Fermi gas " , Physical Review, vol. 104, pp. 1189–1190, 1956. 1956 Bound electron pairs in a degenerate Fermi gas T. P. Eggarter, " Cayley trees, the Ising problem, and the thermodynamic limit " , Physical Review B, vol. 9, pp. 2989–2992, 1974. 1974 Cayley trees, the Ising problem, and the thermodynamic limit J. P. Boyd, Chebyshev and Fourier Spectral Methods. Dover Publications, second ed., 2001. Curriculum Vitae Persönliches Name Daniel Friedrich Ruhl Geburtstag 18.10.1978 1978 Chebyshev and Fourier Spectral Methods Curriculum Vitae Persönliches Name Daniel Friedrich Ruhl Geburtstag 18 S. Lang, ed., Complex Analysis, vol. 103 of Graduate Texts in Mathematics. Springer, fourth ed., 1999. 1999 Complex Analysis E. Müller-Hartmann, " Correlated fermions on a lattice in high dimensions " , Zeitschrift für Physik B: Condensed Matter, vol. 74, pp. 507–512, 1989. 1989 Correlated fermions on a lattice in high dimensions W. Metzner and D. Vollhardt, " Correlated lattice fermions in d = ∞ dimensions " , Physical Review Letters, vol. 62, pp. 324–327, 1989. 1989 Correlated lattice fermions in d = ∞ dimensions L. Onsager, " Crystal statistics. I. A two-dimensional model with an order-disorder transition " , Physical Review, vol. 65, pp. 117–149, 1944. 1944 Crystal statistics. I. A two-dimensional model with an order-disorder transition Diplomarbeit mit dem Titel Ground-State Properties of Correlated Electron Systems in the Limit of High Spatial Dimensions in der AG Vielteilchentheorie des Fachbereichs Physik der Philipps-Universität Marburg unter der Betreuung von Prof. Dr. Florian Gebhard 12/2006 2006 Diplomarbeit mit dem Titel Ground-State Properties of Correlated Electron Systems in the Limit of High Spatial Dimensions in der AG Vielteilchentheorie des Fachbereichs Physik der Philipps N. F. Mott and R. Peierls, " Discussion of the paper by de Boer and Verwey " , Proceedings of the Physical Society, vol. 49, no. 4S, p. 72, 1937. 1937 Discussion of the paper by de Boer and Verwey Doktorand in der AG Vielteilchentheorie des Fachbereichs Physik der Philipps-Universität Marburg Doktorand in der AG Vielteilchentheorie des Fachbereichs Physik der Philipps S. Nishimoto, F. Gebhard, and E. Jeckelmann, " Dynamical density-matrix renormalization group for the Mott-Hubbard insulator in high dimensions " , Journal of Physics: Condensed Matter, vol. 16, pp. 7063–7081, 2004. 2004 Dynamical density-matrix renormalization group for the Mott-Hubbard insulator in high dimensions A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, " Dynamical Mean-Field Theory of strongly correlated Fermion systems and the limit of infinite dimensions " , Reviews of Modern Physics, vol. 68, pp. 13–125, 1996. 1996 Dynamical Mean-Field Theory of strongly correlated Fermion systems and the limit of infinite dimensions E. N. Economou, Green's Functions in Quantum Physics. Springer Series in Solid-State Sciences, Springer, third ed., 2006. 2006 Economou, Green's Functions in Quantum Physics M. C. Gutzwiller, " Effect of correlation on the ferromagnetism of transition metals " , Physical Review Letters, vol. 10, pp. 159–162, 1963. 1963 Effect of correlation on the ferromagnetism of transition metals P. Tittmann, Einführung in die Kombinatorik. Spektrum-Hochschultaschenbuch, Spektrum Akademischer Verlag, 2007. 2007 Einführung in die Kombinatorik. Spektrum-Hochschultaschenbuch J. Kanamori, " Electron correlation and ferromagnetism of transition metals " , Progress of Theo- retical Physics, vol. 30, pp. 275–289, 1963. 1963 Electron correlation and ferromagnetism of transition metals J. Hubbard, " Electron correlations in narrow energy bands. " , Proceedings of the Royal Society, vol. 276, pp. 238–257, 1963. 1963 Electron correlations in narrow energy bands R. Haydock, V. Heine, and M. J. Kelly, " Electronic structure based on the local atomic environ- ment for tight-binding bands " , Journal of Physics C: Solid State Physics, vol. 5, no. 20, p. 2845, 1972. 1972 Electronic structure based on the local atomic environment for tight-binding bands J. M. Ziman, Electrons and Phonons. Oxford Classic Texts in the Physical Sciences, Oxford University Press, 2004. 2004 Electrons and Phonons. Oxford Classic Texts in the Physical Sciences J. D. Cloizeaux, " Energy bands and projection operators in a crystal: Analytic and asymptotic properties " , Physical Review, vol. 135, pp. A685–A697, 1964. 1964 Energy bands and projection operators in a crystal: Analytic and asymptotic properties G. D. Mahan, " Energy bands of the Bethe lattice " , Physical Review B, vol. 63, p. 155110, 2001. 2001 Energy bands of the Bethe lattice C.-K. Hu and N. S. Izmailian, " Exact correlation functions of Bethe lattice spin models in external magnetic fields " , Physical Review E, vol. 58, pp. 1644–1653, 1998. 1998 Exact correlation functions of Bethe lattice spin models in external magnetic fields R. J. Baxter, Exactly Solved Models in Statistical Mechanics. Dover Publications, Inc., 2007. 2007 Exactly Solved Models in Statistical Mechanics J. M. Luttinger, " Fermi surface and some simple equilibrium properties of a system of interacting fermions " , Physical Review, vol. 119, pp. 1153–1163, 1960. 1960 Fermi surface and some simple equilibrium properties of a system of interacting fermions J. L. Gross and J. Yellen, Graph Theory and its Applications. Discrete Mathematics and its Applications, Chapman & Hall/CRC, second ed., 2006. 2006 Graph Theory and its Applications F. Harary, Graph theory and theoretical physics. Academic Press, 1967. 1967 Graph theory and theoretical physics M. Kollar, M. Eckstein, K. Byczuk, N. Blümer, P. van Dongen, M. R. de Cuba, W. Metzner, D. Tanaskovi´Tanaskovi´c, V. Dobrosavljevi´Dobrosavljevi´c, G. Kotliar, and D. Vollhardt, " Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice " , Annalen der Physik, vol. 14, no. 9-10, pp. 642–657, 2005. 2005 Green functions for nearestand next-nearest-neighbor hopping on the Bethe lattice M. Takahashi, " Half-filled Hubbard model at low temperature " , Journal of Physics C: Solid State Physics, vol. 10, pp. 1289–1301, 1977. 1977 Half-filled Hubbard model at low temperature M.-S. Chen, L. Onsager, J. Bonner, and J. Nagle, " Hopping of ions in ice " , The Journal of Chemical Physics, vol. 60, no. 2, pp. 405–419, 1974. 1974 Hopping of ions in ice M. Jarrell, " Hubbard model in infinite dimensions: A quantum Monte Carlo study " , Physical Review Letters, vol. 69, pp. 168–171, 1992. Bibliography [116] A. Georges and G. Kotliar, " Hubbard model in infinite dimensions " , Physical Review B, vol. 45, pp. 6479–6483, 1992. 1992 Hubbard model in infinite dimensions: A quantum Monte Carlo study Hubbard model in infinite dimensions O. Madelung, Introduction to Solid-State Theory. Springer Series in Solid-State Sciences, Springer, 1995. 1995 Introduction to Solid-State Theory D. Vollhardt, " Investigation of correlated electron systems using the limit of high dimensions " , in Correlated Electron Systems: Jerusalem, Israel, 30 Dec 91-8 Jan 92 (Jerusalem Winter School for Theoretical Physics) (V. J. Emery, ed.), p. 57, World Scientific Publishing Co. Pte. Ltd, 1993. 1993 Investigation of correlated electron systems using the limit of high dimensions C. J. Thompson, " Ising model in the high density limit " , Communications in Mathematical Physics, vol. 36, pp. 255–262, 1974. 1974 Ising model in the high density limit T. Morita and T. Horiguchi, " Lattice Green's functions for the cubic lattices in terms of the complete elliptic integral " , Journal of Mathematical Physics, vol. 12, no. 6, pp. 981–986, 1971. Bibliography [40] G. S. Joyce, " Lattice Green function for the simple cubic lattice " , Journal of Physics A: General Physics, vol. 5, no. 8, pp. L65–L68, 1972. 1971 Lattice Green's functions for the cubic lattices in terms of the complete elliptic integral Lattice Green function for the simple cubic lattice J. L. Beeby, " Localization on a Bethe lattice " , Journal of Physics C: Solid State Physics, vol. 6, no. 14, pp. L283–L287, 1973. 1973 Localization on a Bethe lattice M. R. Zirnbauer, " Localization transition on the Bethe lattice " , Physical Review B, vol. 34, pp. 6394–6408, 1986. 1986 Localization transition on the Bethe lattice A. M. Clogston, B. T. Matthias, M. Peter, H. J. Williams, E. Corenzwit, and R. C. Sherwood, " Lo- cal magnetic moment associated with an iron atom dissolved in various transition metal alloys " , Physical Review, vol. 125, pp. 541–552, 1962. 1962 Local magnetic moment associated with an iron atom dissolved in various transition metal alloys F. Yndurain, R. Barrio, R. J. Elliott, and M. F. Thorpe, " Long-range correlations in Bethe lattices " , Physical Review B, vol. 28, pp. 3576–3578, 1983. 1983 Long-range correlations in Bethe lattices R. O. Zaitsev and M. I. Dushenat, " Magnetic and Mott transition in the Hubbard model " , Soviet physics–Solid state, vol. 25, no. 11, p. 1979, 1984. 1984 Magnetic and Mott transition in the Hubbard model B. T. Matthias, M. Peter, H. J. Williams, A. M. Clogston, E. Corenzwit, and R. C. Sherwood, " Magnetic moment of transition metal atoms in dilute solution and their effect on superconducting transition temperature " , Physical Review Letters, vol. 5, pp. 542–544, 1960. 1960 Magnetic moment of transition metal atoms in dilute solution and their effect on superconducting transition temperature H. Bruus and K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics. Oxford Graduate Texts, Oxford University Press, first ed., 2004. 2004 Many-Body Quantum Theory in Condensed Matter Physics. Oxford Graduate Texts G. D. Mahan, Many-Particle Physics. Physics of Solids and Liquids, Plenum Press, second ed., 1990. 1990 Many-Particle Physics. Physics of Solids and Liquids W. Heisenberg, " Mehrkörperproblem und Resonanz in der Quantenmechanik " , Zeitschrift für Physik, vol. 38, pp. 411–426, 1926. 1926 Mehrkörperproblem und Resonanz in der Quantenmechanik M. Imada, A. Fujimori, and Y. Tokura, " Metal-insulator transitions " , Reviews of Modern Physics, vol. 70, no. 4, pp. 1039–1263, 1998. 1998 Metal-insulator transitions J. Friedel, " Metallic alloys " , Supplemento del Il Nuovo Cimento, vol. 7, no. 0, pp. 287–311, 1958. 1958 Metallic alloys J. E. Hirsch and R. M. Fye, " Monte Carlo method for magnetic impurities in metals " , Physical Review Letters, vol. 56, no. 23, pp. 2521–2524, 1986. 1986 Monte Carlo method for magnetic impurities in metals E. Müller-Hartmann and J. Zittartz, " New type of phase transition " , Physical Review Letters, vol. 33, pp. 893–897, 1974. 1974 New type of phase transition V. Fock, " Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems " , Zeit- schrift für Physik, vol. 61, pp. 126–148, 1930. 1930 Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems J. C. Slater, " Note on Hartree's method " , Physical Review, vol. 35, pp. 210–211, 1930. 1930 Note on Hartree's method P. Fazekas, Lecture Notes on Electron Correlation and Magnetism, vol. 5 of Series in Modern Condensed Matter Physics. World Scientific Publishing Co. Pte. Ltd, 1999. 1999 of Series in Modern Condensed Matter Physics H. Fehske, R. Schneider, and A. Weiße, eds., Computational Many-Particle Physics, vol. 739 of The Lecture Notes in Physics. Springer, 2008. 2008 of The Lecture Notes in Physics T. Kato, " On the convergence of the perturbation method I " , Progress of Theoretical Physics, vol. 4, pp. 514–523, 1949. 1949 On the convergence of the perturbation method I C. Domb, " On the theory of cooperative phenomena in crystals " , Advances in Physics, vol. 9, pp. 149–244, 1960. 1960 On the theory of cooperative phenomena in crystals N. F. Mott, " On the transition to metallic conduction in semiconductors " , Canadian Journal of Physics, vol. 34, pp. 1356–1368, 1956. 1956 On the transition to metallic conduction in semiconductors Z. Q. Zhang, T. C. Li, and F. C. Pu, " Percolation on a Bethe lattice with multi-neighbour bonds– exact results " , Journal of Physics A: Mathematical and General, vol. 16, no. 10, pp. 2267–2280, 1983. 1983 Percolation on a Bethe lattice with multi-neighbour bonds– exact results T. Kato, Perturbation theory for linear operators, vol. 132 of Die Grundlehren der mathemati- schen Wissenschaften in Einzeldarstellung mit besonderer Berücksichtigung der Anwendungsge- biete. Springer, 1966. 1966 Perturbation theory for linear operators J. W. Negele and H. Orland, Quantum Many-Particle Systems. Advanced Book Classics, Westview Press, 1998. 1998 Quantum Many-Particle Systems A. Bohm, Quantum Mechanics–Foundations and Applications. Texts and Monographs in Physics, Springer, third ed., 2001. 2001 Quantum Mechanics–Foundations and Applications. Texts and Monographs in Physics T. Giamarchi, Quantum Physics in One Dimension. The International Series of Monographs in Physics, Oxford University Press, 2004. 2004 Quantum Physics in One Dimension. The International Series of Monographs in Physics A. M. Zagoskin, Quantum Theory of Many-Body Systems. Graduate Texts in Contemporary Physics, Springer, 1998. 1998 Quantum Theory of Many-Body Systems. Graduate Texts in Contemporary Physics A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems. Dover Publicatons Inc., 2003. 2003 Quantum Theory of Many-Particle Systems Diplom für Physik ( " sehr gut – mit Auszeichnung " ) seit 01/2007 2007 sehr gut – mit Auszeichnung " ) seit 01 J. H. de Boer and E. J. W. Verwey, " Semi-conductors with partially and with completely filled 3d-lattice bands " , Proceedings of the Physical Society, vol. 49, no. 4S, p. 59, 1937. 1937 Semi-conductors with partially and with completely filled 3d-lattice bands W. F. Brinkman and T. M. Rice, " Single-particle excitations in magnetic insulators " , Physical Review B, vol. 2, pp. 1324–1338, 1970. 1970 Single-particle excitations in magnetic insulators A. B. Harris and R. V. Lange, " Single-particle excitations in narrow energy bands " , Physical Review, vol. 157, pp. 295–314, 1967. 1967 Single-particle excitations in narrow energy bands N. W. Ashcroft and N. D. Mermin, Solid State Physics. Thomson Learning, 1975. 1975 Solid State Physics M. E. Fisher and J. W. Essam, " Some cluster size and percolation problems " , Journal of Mathe- matical Physics, vol. 2, no. 4, pp. 609–619, 1961. 1961 Some cluster size and percolation problems S. Doniach and E. H. Sondheimer, Green's Functions for Solid State Physicists. Imperial College Press, Imperial College Press ed., 1998. Bibliography [77] P. W. Anderson, " Localized magnetic states in metals " , Physical Review, vol. 124, pp. 41–53, 1961. 1961 Sondheimer, Green's Functions for Solid State Physicists. Imperial College Press, Imperial College Press ed Localized magnetic states in metals G. Mussardo, Statistical Field Theory. Oxford University Press, 2009. 2009 Statistical Field Theory C. Itzykson and J.-M. Drouffe, Statistical Field Theory, Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Cambridge University Press, 1991. 1991 Statistical Field Theory From Brownian Motion to Renormalization and Lattice Gauge Theory R. Brout, " Statistical mechanical theory of ferromagnetism. High density behavior " , Physical Review, vol. 118, pp. 1009–1019, 1960. 1960 Statistical mechanical theory of ferromagnetism. High density behavior H. A. Bethe, " Statistical theory of superlattices " , Proceedings of the Royal Society of London. Series A -Mathematical and Physical Sciences, vol. 150, no. 871, pp. 552–575, 1935. 1935 Statistical theory of superlattices –03/2010 Stipendiat des Europäischen Graduiertenkollegs Electron-Electron Interactions in Solids der DFG 08/2009–10/2009 Forschungsaufenthalt mit Prof. Dr. Fabian Essler am Rudolf Peierls Centre for Theo- retical Physics in Oxford, United Kingdom seit 04/2010 2009 Stipendiat des Europäischen Graduiertenkollegs Electron-Electron Interactions in Solids der DFG 08 D. Vollhardt, " Strong-coupling approaches to correlated fermions. " , in Proceedings of the Inter- national School of Physics 'Enrico Fermi', Course CXXI: 'Perspectives in many-particle physics' (Varenna on Lake Como, Villa Monastero, 7-17 July 1992) (R. A. Broglia, J. R. Schrieffer, and P. F. Bortignon, eds.), p. 31, North-Holland Publishing Co., 1994. 1992-07-17 Strong-coupling approaches to correlated fermionsEnrico Fermi', Course CXXI: 'Perspectives in many-particle physics' (Varenna on Lake Como S. Pairault, D. Sénéchal, and A.-M. S. Tremblay, " Strong-coupling expansion for the Hubbard model " , Physical Review Letters, vol. 80, pp. 5389–5392, 1998. 1998 Strong-coupling expansion for the Hubbard model S. Pairault, D. Sénéchal, and A.-M. S. Tremblay, " Strong-coupling perturbation theory of the Hubbard model " , European Physical Journal B, vol. 16, pp. 85–105, 2000. 2000 Strong-coupling perturbation theory of the Hubbard model F. Yndurain, " Surface magnetic order in the Ising model: A Cayley tree approximation " , Physics Letters A, vol. 62, no. 2, pp. 93–94, 1977. 1977 Surface magnetic order in the Ising model: A Cayley tree approximation I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products. Academic Press, sixth ed., 2000. 2000 Table of Integrals, Series, and Products N. F. Mott, " The basis of the electron theory of metals, with special reference to the transition metals " , Proceedings of the Physical Society. Section A, vol. 62, no. 7, pp. 416–422, 1949. 1949 The basis of the electron theory of metals, with special reference to the transition metals D. M. Edwards and L. A. Hertz, " The breakdown of Fermi liquid theory in the Hubbard model " , Physica B: Condensed Matter, vol. 163, no. 1-3, pp. 527–529, 1990. 1990 The breakdown of Fermi liquid theory in the Hubbard model G. C. Wick, " The evaluation of the collision matrix " , Physical Review, vol. 80, pp. 268–272, 1950. [27] T. Koopmans, " ¨ Uber die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms " , Physica, vol. 1, no. 1-6, pp. 104–113, 1934. 1934 The evaluation of the collision matrix E. Müller-Hartmann, " The Hubbard model at high dimensions: some exact results and weak coupling theory " , Zeitschrift für Physik B: Condensed Matter, vol. 76, pp. 211–217, 1989. Bibliography [97] W. Metzner, " Linked-cluster expansion around the atomic limit of the Hubbard model " , Physical Review B, vol. 43, pp. 8549–8563, 1991. 1989 The Hubbard model at high dimensions: some exact results and weak coupling theory Linked-cluster expansion around the atomic limit of the Hubbard model A. C. Hewson, The Kondo Problem to Heavy Fermions. Cambridge Studies in Magnetism, Cam- bridge University Press, 1997. 1997 The Kondo Problem to Heavy Fermions. Cambridge Studies in Magnetism F. Gebhard, The Mott Metal-Insulator Transition, vol. 137 of Springer Tracts in Modern Physics. Springer, 1997. 1997 The Mott Metal-Insulator Transition of Springer Tracts in Modern Physics F. H. L. Essler, H. Frahm, F. Göhmann, A. Klümper, and V. E. Korepin, The One-Dimensional Hubbard Model. Cambridge University Press, 2005. 2005 The One-Dimensional Hubbard Model J. Bardeen, L. N. Cooper, and J. R. Schrieffer, " Theory of superconductivity " , Physical Review, vol. 108, pp. 1175–1204, 1957. 1957 Theory of superconductivity M. Takahashi, Thermodynamics of One-Dimensional Solvable Models. Cambridge University Press, 1999. 1999 Thermodynamics of One-Dimensional Solvable Models N. F. Mott, " The transition to the metallic state " , Philosophical Magazine, vol. 6, pp. 287–309, 1961. 1961 The transition to the metallic state D. R. Hartree, " The wave mechanics of an atom with a non-coulomb central field. Part I. Theory and methods " , Mathematical Proceedings of the Cambridge Philosophical Society, vol. 24, no. 01, pp. 89–110, 1928. 1928 The wave mechanics of an atom with a non-coulomb central field. Part I. Theory and methods F. Bloch, " ¨ Uber die Quantenmechanik der Elektronen in Kristallgittern " , Zeitschrift für Physik, vol. 52, pp. 555–600, 1929. 1929 ¨ Uber die Quantenmechanik der Elektronen in Kristallgittern H. Lehmann, " ¨ Uber Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder " , Il Nuovo Cimento, vol. 11, no. 4, pp. 342–357, 1954. 1954 ¨ Uber Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder V. Janiš and D. Vollhardt, " Construction of analytically tractable mean-field theories for quan- tum models: I. General formalism with application to the Hubbard model at strong coupling " , Zeitschrift für Physik B: Condensed Matter, vol. 91, pp. 317–323, 1993. 1993 Construction of analytically tractable mean-field theories for quantum models: I. General formalism with application to the Hubbard model at strong coupling M. Koecher, Lineare Algebra und analytische Geometrie. Springer, 1997. 1997 Lineare Algebra und analytische Geometrie P. Drude, " Zur Elektronentheorie der Metalle " , Annalen der Physik, vol. 306, no. 3, pp. 566–613, 1900. 1900 Zur Elektronentheorie der Metalle urn:nbn:de:hebis:04-z2010-03773 opus:2960 Philipps-Universität Marburg Ruhl, Daniel F. Ruhl Daniel F. ths Prof. Dr. Gebhard Florian Gebhard, Florian (Prof. Dr.)
recordtype opus
id urn:nbn:de:hebis:04-z2010-0377
urn_str urn:nbn:de:hebis:04-z2010-03773
collection Monograph
uri_str http://archiv.ub.uni-marburg.de/diss/z2010/0377
callnumber-raw diss/z2010/0377
callnumber-search diss/z2010/0377
callnumber-sort diss/z2010/0377
callnumber-label diss z2010 0377
callnumber-first diss
callnumber-subject diss z2010
_version_ 1563293804062048256
score 9,599496