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Title:  Nonperturbative approaches to strongly correlated electron systems 
Author(s):  Lo, Ka Wai 
Director of Research:  Phillips, Philip W. 
Doctoral Committee Chair(s):  Ryu, Shinsei 
Doctoral Committee Member(s):  Phillips, Philip W.; Cooper, S. Lance; Leigh, Robert G. 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  bosonization
antide Sitter/conformal field theory (AdS/CFT) correspondence pomeranchuk instability NonFermi liquid quantum phase transition 
Abstract:  Strong electron correlation phenomena are ubiquitous, such as unconventional superconductivity and the metalinsulator transitions. Having a proper understanding of strongly correlated electron systems requires a nonperturbative analysis because Fermi liquid theory inevitably breaks down due to the strong correlation. In this thesis, we will study two nonperturbative approaches to tackle strongly correlated electronic system: 1.) multidimensional bosonization and 2.) the AdS/CFT correspondence. Multidimensional bosonization is the generalization of bosonization to spatial dimensions larger than one. The bosonized theory is an effective field theory in terms of the bosonic particlehole fluctuations in different patches of the Fermi surface. The bosonized theory is quadratic and hence can be solved nonperturbatively. The AdS/CFT correspondence is a conjecture that ddimensional field theory is dual to a d+1 dimensional quantum gravitational theory. Problems in strongly coupled field theory then have an equivalent description using weakly interacting gravitational theory, allowing a nonperturbative analysis. Chapter 1 will serve as an introduction. We will review several experiments which show a breakdown of Fermi liquid theory. Formalisms for multidimensional bosonization and the AdS/CFT correspondence will then be reviewed. In chapter 2, the twoorbital Hubbard model with degenerate d{xz} and d{yz} orbitals are investigated. We apply multidimensional bosonization to solve this problem exactly and discover a z=3 overdamped collective modes that emerges at the orbitalordering quantum critical point. These modes modify the singleparticle density of states and lead to nonFermi liquid behavior which can provide a possible explanation for the recently observed zerobias enhancement in the point contact spectroscopy signal on iron pnictides. Chapters 3, 4 and 5 discuss the applications of the AdS/CFT correspondence to model various condensed matter systems. In chapter 3, We consider an interaction term between a bulk spinor field and a gauge field in the ReissnerNordstr\"om AdS background. When the Pauli interaction term is large enough, a dynamical gap is generated and spectral weight transfer is observed in the spectral density, mimicking the behavior of the Hubbard model. We further consider the finite temperature case and discover that the ratio between the dynamical gap and the critical temperature has the same order as that of VO^2. The Pauli coupling is also studied in the superconducting background. Chapter 4 consider the propagation of a neutral scalar field in the geometry called the electron star. The electron star has Lifshitz scaling with finite dynamical critical exponent at the interior, which is suitable for the modeling of quantum criticality and quantum phase transition with a neutral order parameter, for example for antiferromagnetism. We find that the quantum phase transition has the BerezinskiKosterlitzThouless characteristic and the dynamical critical exponent can change across the quantum critical point. In chapter 5, we construct a gravity dual of the nematic phase by studying the condensation of a spintwo field in the SchwarzschildAdS background. The condensation of a spintwo field can distort the rotational symmetry of the Fermi surface as long as the spintwo field is coupled to a probe spinor field in the bulk gravity dual. 
Issue Date:  20140116 
URI:  http://hdl.handle.net/2142/46699 
Rights Information:  Copyright 2013 Ka Wai Lo 
Date Available in IDEALS:  20140116 
Date Deposited:  201312 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois