Huber, Sebastian Albert Erwin (2020): A model study of momentumselective Mott physics: numerical approaches and effective models for holedoped Mott insulators. Dissertation, LMU München: Faculty of Physics 

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Abstract
The Fermi liquid theory is a central concept in modern condensed matter physics used to describe conventional metals. A state of this universality class consists of welldefined quasiparticles, which occupy a finite number of states within a Fermi volume defined in momentum space. According to the Luttinger’s theorem, such a state encloses a Fermi volume proportional to the electron density modulo the filled bands if no symmetry is broken. In the past decades strong deviations from Fermi liquid theory have been observed in the scaling behavior of thermodynamic observables in different materials, among which are for instance cuprates and iron pnictides. This thesis is about two prototypical systems that can not be described by Fermi liquid theory. The first part of this work investigates twodimensional effective models, which are in a Mott insulating state at halffilling and have a finite conductivity when doped with holes. In such a Mott insulating state, the charge carriers are strongly localized due to the Coulomb repulsion. Hence, strong correlations are assumed to have a strong impact on the formation of the ground state, also in the regime of small hole concentration. In a first project we have used a socalled spinon dopon meanfield theory to represent the twodimensional FermiHubbard model with strong onsite repulsive interaction in effective degrees of freedom, in which the holes can be embedded into a quantum spin liquid. The corresponding SU(2) invariant ground state belongs to the class of fractionalized Fermi liquids. In a second project we investigate a quantum dimer model, an effective model based on a Hilbert space spanned by short range singlets and bound states of holes and spins. The focus here is on the calculation of the holepart of the electron spectral function by using exact diagonalization and its comparison with two analytic methods, a diagrammatic computation based on the BetheSalpeter equation and a socalled twomode approximation. The electron spectral function shows a similar analytic form in momentum space between nodal and antinodal point when compared to results from photoemission spectroscopy experiments on cuprates. Furthermore, in a subsequent work we calculate the exact ground state of the quantum dimer model along a certain parameter line. In order to analyze the behavior of the elctron spectral function when increasing the density of holes, we investigate the FermiHubbard model in a current project using a dynamical meanfield approach. To solve the 4site cluster impurity problem, we use a numerical renormalization group approach. However, numerical limitations force us to restrict the analysis to spinpolarized baths. According to the spectral data, the system is similar to the SU(2) invariant case at halffilling in a Mott insulating state and posseses a momentumselective energy gap at finite doping. The topology of the Fermi surface shows a Lifshitz transition when increasing the hole concentration. Here, the curvature of the Fermi surface changes from electron to holelike. For comparison we apply the dynamical meanfield theory also to the quantum dimer model and observe that the electron spectral functions at finite doping are qualitatively similar to that of the twodimensional FermiHubbard model. The second half of the work is about TomonagaLuttinger liquid theory, which is used to describe the lowenergy effective degrees of freedom of onedimensional systems. Here, we first discuss a conceptional extension of the operatorbased bosonization theory for onedimensional systems. This extension is especially suited for inhomogeneous onedimensional systems. First, we investigate a onedimensional system with a local interation potential and compute an exact solution of the single particle propagator at T = 0. The critical exponent of the single particle propagator has an unconventional form as a function of the microscopic TomonagaLuttinger parameters, which is not covered by the original Luttinger paradigm postulated by F. Duncan M. Haldane. In a second project on onedimensional systems, we study the impact of scattering processes among bosonic lowenergy excitations on the thermalization process. Such scattering processes are irrelevant on large length scales, however strongly affect the dynamics. In our analytic analysis we focus on a experimental setup, where a onedimensional Bose gas is instantaneously splitted in two identical, however strongly correlated, halves of onedimensional electronic systems. In the following, the corresponding nonequilibrium state runs through multiple regimes in time, such as a metastable prethermalization regime. However, above a certain threshold in time such scattering processes cause an effective thermalization of the system. In order to demonstrate this, we compute the kinetic equation in the Keldysh field integral formalism from a diagrammatic expansion based on a selfconsistent Born approximation.
Item Type:  Theses (Dissertation, LMU Munich) 

Keywords:  Strong correlated electrons, Cuprates, Dimer model, Numerical Renormalization Group, Dynamical MeanField Theory, Exact diagonalization, BetheSalpether approach 
Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  18. May 2020 
1. Referee:  Punk, Matthias 
MD5 Checksum of the PDFfile:  caec2f47e2dc7a0b38b5db456a34b178 
Signature of the printed copy:  0001/UMC 27134 
ID Code:  26179 
Deposited On:  19. Jun 2020 14:17 
Last Modified:  23. Oct 2020 13:59 