The study of the Hubbard model in three dimensions contains a variety of phases dependent upon the chosen parameters. This thesis shows that there is the indication of a zero temperature phase transition at a finite doping. The Hubbard model has been used to identify a similar quantum critical point in two dimensions. The presented results continue these investigations. The system demonstrates a strange metal phase at finite temperature which cannot be described in term of the conventional Fermi liquid. While there have been extensive studies over the past three decades for such materials in two dimensions, there are few numerical studies in three dimensions. This study strives to identify the existence of the strange metal beyond two dimensions. In this work we present numerical results based on the dynamical cluster approximation to demonstrate the existence of a strange metal phase in three dimensions.
The study of the Hubbard model in three dimensions contains a variety of phases dependent upon the chosen parameters. This thesis shows that there is the indication of a zero temperature phase transition at a finite doping. The Hubbard model has been used to identify a similar quantum critical point in two dimensions. The presented results continue these investigations. The system demonstrates a strange metal phase at finite temperature which cannot be described in term of the conventional Fermi liquid. While there have been extensive studies over the past three decades for such materials in two dimensions, there are few numerical studies in three dimensions. This study strives to identify the existence of the strange metal beyond two dimensions. In this work we present numerical results based on the dynamical cluster approximation to demonstrate the existence of a strange metal phase in three dimensions.
We present a numerical study on non-Fermi liquid behaviour of a three dimensional system. The Hubbard model in a cubic lattice is simulated by the dynamical cluster approximation, in particular the quasi-particle weight is calculated at finite dopings for a range of temperatures. Near the putative quantum critical point, we find evidence of a separatrix at a finite doping which separates the Fermi liquid from non-Fermi liquid as the doping increases. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point should exist in the three dimensions interacting Fermi system.
We study the normal-state, doping-driven phase diagram of the square-lattice Hubbard model using the dynamical cluster approximation combined with the numerical renormalization group as a cluster solver, which gives direct access to real-frequency dynamics at essentially zero temperature. In a parameter regime relevant for cuprates, U=7t and t′=−0.3t, we find a critical doping p∗ that marks a continuous quantum phase transition between a pseudogap metal and a normal Fermi liquid. The transition is identified by a continuous collapse, from both sides, of the Fermi-liquid scale extracted from charge, spin, and dx2−y2-wave pairing susceptibilities. This collapse produces a non-Fermi-liquid regime at intermediate energy scales, which appears to extend to arbitrarily low scales at p∗. As p∗ is crossed from the normal Fermi liquid at p>p∗ into the pseudogap metal at $p
We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.
Materials with strongly correlated electrons show a multitude of unconventional phenomena, such as superconductivity or magnetism, that cannot be explained in a single-particle picture and necessitate to take many-body effects into account. A route to explain the origin of these phenomena consists in constructing effective models for these materials that are then solved, often using numerical techniques. Paradigmatic models for two different classes of strongly correlated electron systems are investigated in this thesis: The Hubbard model is a paradigmatic model to describe the Mott metal-insulator transition (MIT) and the Kondo lattice model describes the low-energy physics in heavy fermion compounds. Both models are analyzed numerically using different variations of a quantum cluster technique, the variational cluster approximation (VCA). The first part focuses on the MIT, as it is investigated experimentally in quasi-two-dimensional charge-transfer salts. Its nature and associated universality class are still heavily discussed and both experiments and theoretical approaches come to different conclusions. In this thesis, the Mott transition is investigated on an anisotropic two-dimensional Hubbard model at half-filling. By using a control parameter, which induces this anisotropy, strong evidence for Mott quantum criticality is found in weakly coupled Hubbard chains. The results at zero temperature show that the second-order critical end point Tc of the interaction-driven metal-insulator transition can be tuned down to zero at strong anisotropy. Further results for the antiferromagnetic phase suggest a similar picture and motivate adding the anisotropy as a new axis in the phase diagram to account for a low-temperature critical end point of the Mott transition. The second part of this thesis focuses on unconventional phases that emerge in a paradigmatic model for heavy fermion systems, the Kondo lattice model. Using the VCA, the two-dimensional Kondo lattice model is investigated in the paramagnetic phase as well as in phases with broken symmetry. An antiferromagnetic phase at weak coupling and a phase with Kondo-singlet formation at strong coupling are analyzed. Within the antiferromagnetically ordered region, two phases with different Fermi-surface topology, which are separated by a discontinuous transition, are identified. The model is also tested for s-wave superconductivity as found recently using dynamical mean-field theory, but no indications for robust local pairing are seen within VCA. Instead, nodal d-wave superconductivity is found and analyzed in a large range of couplings and electron fillings, and its interplay with antiferromagnetic order at weak coupling is discussed. This motivates further studies on extended models that might allow for a close comparison with experiments on heavy fermion systems. Understanding the formation of unconventional phases in strongly correlated electron systems is not only of fundamental interest, but it is also essential for designing new functional materials. Although the results of approximate cluster techniques have to be handled with care, the new aspects presented in this thesis pave the way for further investigations in this direction.
Many strongly correlated systems exhibit strange metallic behavior in certain parameter regimes characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. The Hubbard model is a standard theoretical starting point to examine the properties of such systems and also exhibits non-Fermi-liquid behavior in simulations. Here we analytically study the two-dimensional hole-doped Hubbard model in the large U limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping pc depending on lattice structure. Using the critical properties near this transition we rewrite the Hubbard Hamiltonian and motivate a low-energy lattice-independent large-N model with distinct non-Fermi-liquid properties. We show that this model has linear-in-T resistivity with doping-dependent slope maximized at p=pc and power-law optical conductivity ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$. Though the parameters used in developing this theory mean it cannot be directly applied to the cuprate superconductors, we nevertheless reproduce several important phenomena observed in their strange metal phase and also predict these same qualitative behaviors to manifest in other lattices near concrete hole dopings.
In this thesis, we develop a dynamical mean field approach to strongly correlated electron systems. Our approach is based on the standard limit of infinite dimensions but goes beyond that by treating inter-unit-cell interactions on an equal footing with inter-unit-cell ones. We apply this approach to several systems, including the Kondo lattice model and the extended Hubbard model. For the extended Hubbard model, we find that certain non-Fermi liquid states survive in the presence of intra-unit-cell interactions. Our results provide the first step towards establishing the relevance of these states to physical systems in finite dimensions. For the Kondo lattice model, we identify a novel quantum critical point where the local Kondo dynamics is also critical. This novel critical point appears to describe what happens in certain heavy fermion metals close to a magnetic phase transition.