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.
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.
In this thesis, several cases of non-equilibrium phenomena and quantum phase transitions in strongly correlated electron systems are analyzed. The unconventional critical behavior near magnetic quantum phase transitions in various heavy-fermion metals has triggered proposals on the breakdown of the Kondo effect at the critical point. In part I, we investigate, within one specific scenario, the fate of such a zero-temperature transition upon coupling of the electronic to lattice degrees of freedom. We study a Kondo-Heisenberg model with volume-dependent Kondo coupling � this model displays both Kondo volume collapse and Kondo-breakdown transitions. Within a large-N treatment, we find that the Kondo breakdown transition remains of second order except for very soft lattices. Finally, we relate our findings to current heavy-fermion experiments. Using non-equilibrium Green�s functions, we derive transport equations for the degrees of freedom participating in the quantum critical region of the Kondo breakdown transition. We discuss conditions under which the transport of electrical charge is described by the independent motion of conduction electrons and auxiliary bosons. Under these conditions, we derive a semiclassical transport equation for the bosons and quantitatively discuss the electrical conductivity of the whole system. Motivated by pressure experiments on FeAs-122 superconductors, in part II we propose a scenario based on local-moment physics to explain salient features at the magnetic phase boundary of CaFe2As2. In this scenario, the low-pressure magnetic phase derives from Fe moments, which become screened in the paramagnetic high-pressure phase. The quantum phase transition can be described as an orbital-selective Mott transition, which is rendered first order by coupling to the lattice. These ideas are illustrated by a suitable mean-field analysis of an Anderson lattice model. An analytical description of non-equilibrium phenomena in interacting quantum systems is rarely possible. In part III we present one example where such a description can be achieved, namely the ferromagnetic Kondo model. In equilibrium, this model is tractable via perturbative renormalization-group techniques. We employ a recently developed extension of the flow-equation method to calculate the non-equilibrium decay of the local magnetization at zero temperature. The flow equations admit analytical solutions which become exact at short and long times, in the latter case revealing that the system always retains a memory of its initial state. Finally, in part IV we analyze the Nernst effect resulting from normal state quasiparticles in the cuprates in presence of various types of translational symmetry breaking. In the electron-doped cuprates, the Nernst signal resulting from a reconstruction of the Fermi surface due to spin density wave order is discussed. An order parameter consistent with the reconstruction of the Fermi surface detected in electron-doped materials is shown to sharply enhance the Nernst signal close to optimal doping. Within a semiclassical treatment, the obtained magnitude and position of the enhanced Nernst signal agrees with Nernst measurements in electron-doped cuprates. In the hole-doped cuprates, we discuss relations between the normal-state Nernst effect and stripe order. We find that Fermi pockets caused by translational symmetry breaking lead to a strongly enhanced Nernst signal with a sign depending on the modulation period of the ordered state and other details of the Fermi surface. This implies differences between antiferromagnetic and charge-only stripes. We compare our findings with recent data from La1.6−xNd0.4SrxCuO4 and YBa2Cu3Oy.
Strongly correlated electron systems show a rich variety of astonishing physical phenomena. However, the strong interactions make the theoretical description of these systems a highly non-trivial task. Even the simplest models cannot be solved exactly, and one has to reside to approximative solutions, which often cover only certain aspects of the physics contained in these models. In recent years progress has been made in the theoretical description of correlated lattice systems through the mapping of lattice models onto effective impurity models. The most prominent example is the mapping of the Hubbard model onto an effective single impurity Anderson model (SIAM). Within this description both models feature the prominent Kondo effect, which leads to the emergence of low energy quasiparticles. The occurrence of such excitations is a result of the dynamical screening of local magnetic moments and the corresponding formation of a low temperature Fermi liquid phase. On the other hand these theories usually fail in the description of non Fermi liquid behavior, which is for example observed in the normal state of high temperature superconductors and some Heavy-Fermion systems. Strong nonlocal fluctuations drive the dynamics of these systems. In the theoretical treatment, due to the mapping of the lattice problem to an effective single impurity problem, these fluctuations are not adequately described.\\\\ In this thesis a new self-consistent approach for the inclusion of spatial correlations is presented for the Hubbard model. In contrast to existing quantum cluster theories in this field, the approach allows for the simultaneous description of short and long range pair correlations. Due to the intimate connection of this new lattice theory with the two impurity Anderson model (TIAM) a thorough numerical investigation of the TIAM is undertaken in this thesis. The competition of the Kondo effect with the RKKY interactions is studied in great detail. Furthermore two new solvers for the TIAM are introduced, which extend existing non crossing approximations for the SIAM.
Strongly correlated electron systems show a rich variety of interesting physical phenomena. However, their theoretical description poses a highly non-trivial task, and even the simplest models cannot be solved exactly. In this thesis the intricate behavior of the single impurity Anderson model (SIAM) and the Hubbard model is investigated. The main emphasis is laid on two-particle Green functions of these systems. To this end, existing approximation schemes are extended to be capable of treating susceptibilities as well. The quality and range of applicability of these approximations is discussed in detail. The physical pictures behind the phenomena encountered in these systems are introduced. A prominent many-body effect is the emergence of temperature dependent low energy quasiparticles in both models. The occurrence of such excitations is a result of the dynamical screening of local magnetic moments, a characteristic feature of the Kondo effect. It is argued, that within the presented approximations, the low temperature phase of these models can usually be described as a Fermi liquid. As a counterexample, the Hubbard model is shown to exhibit pronounced non-Fermi liquid behavior in situations, where a van Hove singularity in the non-interacting density of states is found in the vicinity of the Fermi level. The magnetic properties of the Hubbard model are discussed in view of the two archetypical pictures of magnetism: local moment magnetism and itinerant Stoner-magnetism. Critical temperatures for antiferromagnetic, ferromagnetic and incommensurate phase transitions are calculated, and the influence of the lattice structure and frustration is examined. In strongly correlated metallic situations, the complicated competition between Kondo-screening and local moment magnetism can lead to a reentrant behavior of the N\'eel temperature. A direct signature of the Kondo effect in the Hubbard model is found in the dynamic magnetic susceptibility, where a localized collective mode emerges at very low temperatures. It is connected to the breakup of a singlet formed by the local moments with their Kondo-screening cloud, and consequently the excitation energy is of the order of the low energy scale T*.
Abstract The theory of quantum critical phenomena is introduced to study some current many-body problems in condensed matter physics. Renormalization group concepts are applied to strongly correlated electronic materials which are close to a zero-temperature instability. These systems have enhanced effective masses and susceptibility. Scaling arguments yield the exponents which govern the critical behavior of these quantities in terms of the usual critical exponents associated with a zero-temperature phase transition. We show the existence of a new energy scale, related to the quantum nature of the many-body instability, which can be generally associated with the setting of Fermi-liquid behavior with decreasing temperature in three-dimensional strongly interacting electronic systems. The theory of quantum critical phenomena is used to investigate the Kondo lattice problem, which provides a model to describe heavy-fermion systems and to introduce a scaling theory of the Mott transition with special emphasis on charge fluctuation effects. However, this report is not a review on heavy fermions and Mott insulators. The microscopic theories of these systems are still controversial and present some of the most challenging and instigating problems in condensed matter physics. This state of affairs stimulated the author to review and extend the scaling approach. The scaling theory we develop provides a powerful tool, based on the notion of universality, to understand the physical properties of correlated systems beyond the mean-field level. This is illustrated by our treatment of the one-dimensional Hubbard model, where, although the Fermi-liquid fixed point does not survive the fluctuations, the scaling approach is still useful. Finally, we discuss briefly how disorder affect our results.
Abstract The theory of quantum critical phenomena is introduced to study some current many-body problems in condensed matter physics. Renormalization group concepts are applied to strongly correlated electronic materials which are close to a zero-temperature instability. These systems have enhanced effective masses and susceptibility. Scaling arguments yield the exponents which govern the critical behavior of these quantities in terms of the usual critical exponents associated with a zero-temperature phase transition. We show the existence of a new energy scale, related to the quantum nature of the many-body instability, which can be generally associated with the setting of Fermi-liquid behavior with decreasing temperature in three-dimensional strongly interacting electronic systems. The theory of quantum critical phenomena is used to investigate the Kondo lattice problem, which provides a model to describe heavy-fermion systems and to introduce a scaling theory of the Mott transition with special emphasis on charge fluctuation effects. However, this report is not a review on heavy fermions and Mott insulators. The microscopic theories of these systems are still controversial and present some of the most challenging and instigating problems in condensed matter physics. This state of affairs stimulated the author to review and extend the scaling approach. The scaling theory we develop provides a powerful tool, based on the notion of universality, to understand the physical properties of correlated systems beyond the mean-field level. This is illustrated by our treatment of the one-dimensional Hubbard model, where, although the Fermi-liquid fixed point does not survive the fluctuations, the scaling approach is still useful. Finally, we discuss briefly how disorder affect our results.