A multiorbital quantum impurity with effective spin S>1/2 connected to several reservoirs of conduction electrons can lead to a Kondo effect, exhibiting multistage screening. The ground state of a prototypical nanoscale device consisting of an S=1 quantum impurity connected to two conducting reservoirs is a spin singlet, formed via a two-stage Kondo screening mechanism. Understanding the equilibrium and nonequilibrium properties of the strong-coupling regime resulting from this two-stage screening has been an open problem for many years. Here, the authors offer a detailed description in terms of an effective local two-color Fermi liquid theory.
Modern quantum materials host a wide range of electronic phases in which transport properties are governed by strong interactions and collective effects. This thesis investigates charge, heat, and momentum transport in interacting electronic systems across different theoretical frameworks, ranging from Fermi liquid theory to strongly coupled strange metals.The first part of the thesis focuses on two-dimensional Fermi liquids at finite temperature, where rapid electron-electron scattering can give rise to hydrodynamic behavior. A kinetic-theory framework allowing an exact treatment of quasiparticle distribution functions beyond the asymptotic low-temperature regime is used to compute the full spectrum of collective modes, providing a detailed characterization of long-lived odd-parity excitations and the intermediate transport regime between ballistic and hydrodynamic flow. The same framework is employed to determine the shear viscosity of interacting electron liquids beyond conventional perturbative limits.The second part of the thesis concerns strongly interacting quantum systems where the quasiparticle picture breaks down.Holographic duality is used to study transport and thermoelectric response in quantum critical systems subject to periodic potentials, providing a controlled framework for momentum relaxation and magnetotransport in non-Fermi liquids. The thesis further develops holographic models of collective charge dynamics in systems with dynamical electromagnetism, including bulk plasmons and surface plasmon polaritons, and explores connections between Fermi surface physics and holographic gauge-field dynamics.
In this thesis, we describe methods for solving quantum impurity models out of equilibrium, and consider several applications of these methods. Quantum impurity models describe systems in which a small subsystem (the impurity) is coupled to a large external environment (the bath). These models are useful in describing a wide variety of physical systems, including quantum dots, absorbed adatoms, and molecular junctions. They are also important for the study of lattice models, such as the Hubbard model, where they appear as auxiliary problems within the framework of dynamical mean field theory (DMFT). Many interesting phenomena in these systems, such as transport through a quantum dot, or optical pumping of a Mott insulator, occur away from equilibrium. Theoretical description of these phenomena requires methods that are capable of handling both real time evolution and strong correlation effects presenting a formidable challenge. In this thesis, we describe several methods for the solution of non-equilibrium quantum impurity models which meet this challenge. These methods are based on an expansion in the coupling between the impurity and the bath known as the hybridization expansion. Chapter 1 gives an introduction to the problems addressed in this thesis. Chapter 2 provides a brief overview of Keldysh formalism for nonequilibrium problems. Chapter 3 describes the bare hybridization expansion for the Anderson impurity model as well as its bold extensions. In particular we derive the non-crossing approximation (NCA), the one-crossing approximation (OCA), the inchworm expansion, and a bold expansion for the impurity Green's function. Chapter 4 describes the implementation of a quantum Monte Carlo algorithm based on the inchworm expansion. The rest of the thesis describes applications of these algorithms to problems of physical interest. Chapters 5 and 6 apply the methods previously described to understanding the Kondo effect in quantum dot systems. The first chapter examines the behavior of the Kondo effect under an applied voltage bias, a classic non-equilibrium strongly-correlated problem. The second chapter examines different ways of measuring the cloud of electrons which screen the impurity spin in the Kondo regime. Chapters 7 and 8 apply the same methods to the Hubbard model using the Dynamical mean-field theory (DMFT) mapping. The first chapter studies the Hubbard model in equilibrium using the numerically exact inchworm quantum Monte Carlo method. The second chapter studies the possibility of dynamic switching between the metal and Mott-insulator states of the Hubbard model using the one-crossing approximation (OCA). Finally chapter 9 gives some overall conclusions and suggests future directions for the development of hybridization expansion methods.
This thesis deals with the study of dynamical properties of out-of-equilibrium quantum systems. We introduce in particular a general class of Spin-Boson models, which describe for example light-matter interaction or dissipative phenomena. We contribute to the development of a stochastic approach to describe the spin dynamics in these models. In this context, the effect of the bosonic environment is encapsulated into additional stochastic degrees of freedom whose time-correlations are determined by spectral properties of the bosonic environment. We use this approach to study many-body phenomena such as the dissipative quantum phase transition induced by an ohmic bosonic environment. Synchronization phenomena as well as dissipative topological transitions are identified. We also progress in the study of arrays of interacting light-matter systems. These theoretical developments follow recent experimental achievements, which could ensure a quantitative study of these phenomena. This notably includes ultra-cold atoms, trapped ions and cavity and circuit electrodynamics setups. We finally investigate hybrid systems comprising electronic quantum dots coupled to electromagnetic resonators, which enable us to provide a spectroscopic analysis of many-body phenomena linked to the Kondo effect. We also introduce thermoelectric applications in these devices.
We present a comprehensive Fermi liquid description for thermoelectric transport and current noise, applicable to multilevel quantum dots (QD) and magnetic alloys (MA) without electron-hole or time-reversal symmetry. Our formulation for the low-energy transport is based on an Anderson model with
N discrete impurity levels, and is asymptotically exact at low energies, up to the next-leading order terms in power expansions with respect to temperature
T and bias voltage
eV. The expansion coefficients can be expressed in terms of the Fermi liquid parameters, which include the three-body correlation functions defined with respect to the equilibrium ground state in addition to the linear susceptibilities and the occupation number
Nd of impurity electrons. We apply this formulation to the
SU(N) symmetric QD and MA, and calculate the correlation functions for
N=4 and 6, using numerical renormalization group approach. The three-body correlations are shown to be determined by a single parameter over a wide range of electron fillings $1\ensuremath{\lesssim}{N}_{d}^{}\ensuremath{\lesssim}N\ensuremath{-}1$ for strong Coulomb interactions
U, and they also exhibit the plateau structures due to the
SU(N) Kondo effects at integer values of
Nd. We find that the Lorenz number $L=\ensuremath{\kappa}/(T\ensuremath{\sigma})$ for QD and MA, defined as the ratio of the thermal conductivity $\ensuremath{\kappa}$ to the electrical conductivity $\ensuremath{\sigma}$, deviates from the universal Wiedemann-Franz value ${\ensuremath{\pi}}^{2}/(3{e}^{2})$ as the temperature increases from
T=0, showing the
T2 dependence, the coefficient for which depends on the three-body correlations away from half filling. Furthermore, we find that the current noise for the SU(4) quantum dots and that for SU(6) show a pronounced difference at the quarter
Nd/N=1/4 and
3/4 fillings. In particular, the linear noise for
N=4 exhibits a flat peak while the peak for
N=6 shows a round shape, reflecting the fact that, at these filling points, the
SU(N) Kondo effects occur for $N\ensuremath{\equiv}0$ (mod 4), whereas the intermediate-valence fluctuations occur for $N\ensuremath{\equiv}2$ (mod 4). We also demonstrate the role of three-body correlations on the nonlinear current noise and the other transport coefficients.
In recent years, nano-sized systems involving local charge or spin states have received wide interests because of their potential application in emerging fields such as quantum information and quantum computation. For instance, organometallic molecular complexes may serve as building blocks of quantum storage devices, because the spin-unpaired d or f electrons at transition metal centers may be employed to construct spin qubits. Moreover, if the system contains strong electron-electron interaction, the involving local quantum states are subject to prominent electron correlation effects (such as the Kondo effect). Theoretically, spatially confined nano-systems are often described by quantum impurity models. Thus the accurate prediction of the intrinsic properties of quantum impurity systems and the deep understanding on the response and evolution of local quantum states under external fields or in dissipative environment are fundamentally important for the design and fabrication of quantum devices. The accurate characterization of quantum coherence, correlation, and entanglement in quantum impurity systems remains a great challenge. Enormous efforts have been made to achieve this goal. A variety of theoretical methods have been developed, including the numerical renormalization group method, the quantum Monte Carlo method, and many others. However, all the existing methods are subject to certain limitations regarding accuracy or efficiency. Therefore, we choose to view this problem from a new perspective—the perspective of open quantum systems. Over the past decade, we have developed a formally exact quantum dissipation theory, the hierarchical equations of motion (HEOM) theory, for fermionic open systems. The HEOM theory captures the combined effects of system-environment dissipation, many-body interaction, and non-Markovian memory in a nonperturbative manner. It is capable of addressing static and dynamic responses of system observables in both equilibrium and nonequilibrium situations. We have implemented the HEOM method in our self-designed computer program HEOM-QUICK. We have also devised a series of advanced algorithms which substantially enhance the numerical efficiency of HEOM. The HEOM-QUICK program thus provides an accurate, efficient, and versatile theoretical tool for the investigation of strongly correlated quantum impurity systems. We have applied the HEOM method to study a variety of problems associated with quantum impurity systems. These include the intrinsic properties of quantum impurity models and lattice models, the transient current response of quantum dots to ac voltages, the thermopower and local heating effect in nonequilibrium quantum dots, and the tuning of local spin states in adsorbed molecular magnets. In particular, the HEOM method has been combined with density functional theory (DFT) method, and thus allows for first-principles-based simulation on the precise tuning of local spin states in adsorbed magnetic molecules. Numerical simulations have discovered or reproduced many important quantum phenomena that are essential for relevant experiments, including the Kondo effect, Mott metal-insulator transition, quantum memristive effect, etc. This paper gives a brief overview of our development of the HEOM method for fermionic open systems, as well as its applications to various strongly correlated quantum impurity systems.