Non-perturbative approaches to strongly correlated electron systems

bosonization;anti-de Sitter/conformal field theory (AdS/CFT) correspondence;pomeranchuk instability;Non-Fermi liquid;quantum phase transition

Lo, Ka Wai

关键词: bosonization;    anti-de Sitter/conformal field theory (AdS/CFT) correspondence;    pomeranchuk instability;    Non-Fermi liquid;    quantum phase transition;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/46699/Ka%20Wai_Lo.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Strong electron correlation phenomena are ubiquitous, such as unconventional superconductivity and the metal-insulator transitions.Having a proper understanding of strongly correlated electron systems requires a non-perturbative analysis because Fermi liquid theory inevitably breaks down due to the strong correlation.In this thesis, we will study two non-perturbative approaches to tackle strongly correlated electronic system:1.) multi-dimensional 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 particle-hole fluctuations in different patches of the Fermi surface. The bosonized theory is quadratic and hence can be solved non-perturbatively.The AdS/CFT correspondence is a conjecture that d-dimensional 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 non-perturbative 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 two-orbital 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 orbital-ordering quantum critical point. These modes modify the single-particle density of states and lead to non-Fermi liquid behavior which can provide a possible explanation for the recently observed zero-bias 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 Reissner-Nordstr\"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 Berezinski-Kosterlitz-Thouless 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 spin-two field in the Schwarzschild-AdS background. The condensation of a spin-two field can distort the rotational symmetry of the Fermi surface as long as the spin-two field is coupled to a probe spinor field in the bulk gravity dual.