We study the microscopic mechanism controlling the interplay between local charge and local spin fluctuations in correlated electron systems via a thorough investigation of the generalized on-site charge susceptibility of several fundamental many-electron models, such as the Hubbard atom, the Anderson impurity model, and the Hubbard model. By decomposing the numerically determined generalized susceptibility in terms of physically transparent single-boson exchange processes, we unveil the microscopic mechanisms responsible for the breakdown of the self-consistent many-electron perturbation expansion. In particular, we unambiguously identify the origin of the significant suppression of its diagonal entries in (Matsubara) frequency space and the slight increase of the off-diagonal ones which cause the breakdown. The suppression effect on the diagonal elements originates directly from the electronic scattering on local magnetic moments, reflecting their increasingly longer lifetime as well as their enhanced effective coupling with the electrons. Instead, the slight and diffuse enhancement of the off-diagonal terms can be mostly ascribed to multiboson scattering processes. The strong intertwining between spin and charge sectors is partly weakened at the Kondo temperature due to a progressive reduction of the effective spin-fermion coupling of local magnetic fluctuations in the low frequency regime. Our analysis, thus, clarifies the precise mechanism through which the physical information is transferred between different scattering channels of interacting electron problems and highlights the pivotal role played by such an intertwining in the physics of correlated electrons beyond the perturbative regime.
We study the microscopic mechanism controlling the interplay between local charge and local spin fluctuations in correlated electron systems via a thorough investigation of the generalized on-site charge susceptibility of several fundamental many-electron models, such as the Hubbard atom, the Anderson impurity model, and the Hubbard model. By decomposing the numerically determined generalized susceptibility in terms of physically transparent single-boson exchange processes, we unveil the microscopic mechanisms responsible for the breakdown of the self-consistent many-electron perturbation expansion. In particular, we unambiguously identify the origin of the significant suppression of its diagonal entries in (Matsubara) frequency space and the slight increase of the off-diagonal ones which cause the breakdown. The suppression effect on the diagonal elements originates directly from the electronic scattering on local magnetic moments, reflecting their increasingly longer lifetime as well as their enhanced effective coupling with the electrons. Instead, the slight and diffuse enhancement of the off-diagonal terms can be mostly ascribed to multiboson scattering processes. The strong intertwining between spin and charge sectors is partly weakened at the Kondo temperature due to a progressive reduction of the effective spin-fermion coupling of local magnetic fluctuations in the low frequency regime. Our analysis, thus, clarifies the precise mechanism through which the physical information is transferred between different scattering channels of interacting electron problems and highlights the pivotal role played by such an intertwining in the physics of correlated electrons beyond the perturbative regime.
We identify the precise hallmarks of the local magnetic moment formation and its Kondo screening in the frequency structure of the generalized charge susceptibility. The sharpness of our identification even pinpoints an alternative criterion to determine the Kondo temperature of strongly correlated systems on the two-particle level, which only requires calculations at the lowest Matsubara frequency. We showcase its strength by applying it to the single impurity and the periodic Anderson model as well as to the Hubbard model. Our results represent a significant progress for the general understanding of quantum field theory at the two-particle level and allow for tracing the limits of the physics captured by perturbative approaches for correlated systems.
Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.
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.
Electronic band structures usually remain unaffected by doping via a chemical-potential shift or by increasing the temperature in conventional band insulators. In contrast, it has been shown that those of Mott and Kondo insulators can be altered by doping or by increasing the temperature: electronic modes are induced within the band gap, exhibiting momentum-shifted magnetic dispersion relations from the band edges. Here, this study demonstrates that the underlying mechanism of the remarkable strong-correlation effects can be generalized to the emergence of electronic modes caused by various spin and charge perturbations, including magnetization of spin-gapped Mott and Kondo insulators. These emergent modes can alter the band structure if a macroscopic number of spins or charges are excited by the perturbations at a given moment. The origins and dispersion relations of these emergent modes, particularly why and how the dispersion relations depend on the momentum and energy of the perturbations, are elucidated by investigating the selection rules and using the Bethe ansatz and the effective theory for weak inter-unit-cell hopping. The validity and generality of the theoretical results across different models and spatial dimensions are verified by numerical calculations for the one- and two-dimensional Hubbard models, periodic Anderson models, Kondo lattice models, and ladder and bilayer Hubbard models. This study provides crucial insights into why and how spin and charge perturbations can alter the band structure in strongly correlated insulators, thereby paving the way for band-structure engineering in strong-correlation electronics, which enables previously unexplored functionalities by exploiting the unconventional characteristics revealed in this paper.
This dissertation examines the impact of long-range interactions in lattice models of low-dimensional strongly correlated systems with a focus on their relevance to anomalous electronic transport. Traditionally, the Hubbard model forms the basis of theoretical and numerical investigations of strongly correlated quantum matter. This effective model constitutes the simplest model of electronic correlation and relies on an approximation that truncates electron-electron interactions to a local, on-site potential. While this approximation has proved valid in several instances, certain unexplained phenomena in correlated materials challenge us to develop new perspectives and approaches.In the first part of this thesis, we discuss the historical motivation for our current work from both a theoretical and an experimental viewpoint. In particular, we cover the discovery of bad metallic transport and the associated breakdown of Boltzmann theory of electron transport. We further review examples of strongly correlated systems that exhibit bad metallic transport and other exotic phenomena that suggest the possibility of poorly screened electronic interactions acting as a common microscopic mechanism. This general feature justifies the development of a theoretical framework that is capable of examining long-range interactions in a controlled, systematic manner.Motivated by this, we analyze a long-range interacting lattice model for spinless electrons in two dimensions via exact diagonalization on a finite cluster in real space. As this method is susceptible to finite-size errors, we discuss at length its implementation and technical details designed specifically to reduce these errors, namely the use of twisted boundary conditions and the Ewald summation. We determine the phase diagram at zero temperature and demonstrate that the long-range interactions act as a source of self-generated disorder that drives the development of a strongly correlated pseudogap phase, in a manner reminiscent of the classical Efros-Shklovskii Coulomb gap. Furthermore, we establish that this phenomenon is independent of lattice geometry, a fact that represents the broad potential of long-range interactions in giving rise to a novel form of strongly correlated behavior.Following our zero-temperature study, we address the question of whether this self-generated disorder can survive in the presence of thermal fluctuations and local Coulomb repulsion (Hubbard terms) relevant in Mott systems, a situation closer to those in experimental systems. By means of classical Monte Carlo calculations, we show that not only does the self-generated disorder survive, but that it also acts as a microscopic mechanism that generates bad metallic transport. Upon further investigation, we determine that the long-range interactions, in combination with quantum fluctuations, cause a transient localization of the charge carriers, thereby suppressing the conductivity values below those predicted in conventional Boltzmann theory, as observed experimentally.In conclusion, we have established that long-range interactions in electronic models act as a microscopic mechanism that is capable of causing exotic phenomena in numerous materials. We conclude that a proper treatment of both quantum fluctuations and long-range interactions should next be studied with the finite temperature Lanczos method, which will act as a bridge between our exact diagonalization and Monte Carlo studies. Overall, this dissertation emphasizes the capability of long-range interactions to produce novel phenomena and elicits further thought-provoking questions concerning the interplay with Mott-Hubbard physics and external disorder, crucial in metallic systems.
Electron-electron and electron-phonon interactions are responsible for the formation of spin, charge, and superconducting correlations in layered quantum materials. A paradigmatic model for such materials that captures both kinds of interactions is the two-dimensional Hubbard-Holstein model with a dispersionless Einstein phonon. In this work, we provide a detailed analysis of the magnetic, density, and superconducting fluctuations at and away from half filling. To that end, we employ the functional renormalization group using the recently introduced extension of the single-boson exchange formulation. More precisely, we go beyond previous approaches to the model by resolving the full frequency dependence of the two-particle vertex and taking into account the feedback from the electronic self-energy. We perform broad parameter scans in the space of Hubbard repulsion, electron-phonon coupling strength, and phonon frequency to explore the leading magnetic, density, and superconducting susceptibilities from the adiabatic to the anti-adiabatic regime. Our numerical data reveal that self-energy effects lead to an enhancement of the d -wave superconducting susceptibility toward larger phonon frequencies, in contrast to earlier isotope-effect studies. At small phonon frequencies, large density contributions to the s -wave superconducting susceptibility change sign and eventually lead to a reduction of s -wave superconductivity with increasing electron-phonon coupling, signaling the breakdown of Migdal-Eliashberg theory. We analyze our findings systematically, employing detailed diagnostics of the intertwined fluctuations and pinning down the various positive and negative isotope effects of the physical susceptibilities. Our results pave the way for a more comprehensive understanding of the interplay of electron-electron and electron-phonon interactions in correlated quantum materials.