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A detailed experimental study has been made of the spin-splitting factors ℊc for magnetic Landau levels associated with conduction electrons in extremal orbits on the Fermi surface of lead. This information has been derived from the waveform of the de Haas-van Alphen (dHvA) quantum oscillations in the magnetization of single-crystal lead spheres at temperatures of about 1.2 K and with applied magnetic fields in the range 50-75 kG. A commercial spectrum analyzer has been used to provide on-line values of the harmonic amplitudes in the dHvA waveform, and the values of ℊc have been extracted from the relative strengths of the harmonics. Serious systematic errors in ℊc can arise on account of waveform distortions caused by the small and subtle difference between the externally applied field H and the magnetizing field B acting on the conduction electrons. In 1981 Gold and Van Schyndel demonstrated that these 'magnetic-interaction' distortions could be suppressed to a large extent by using negative magnetic feedback to make the induction B within the sample be the same as H (or very nearly so). This thesis describes the first in-depth application of the magnetic-feedback technique to the systematic study of any metal. Particular attention has been paid to the effect of sample inhomogeneity, and Shoenberg's treatment of the magnetic interaction in a non-uniform sample has been generalized to include magnetic feedback. This theory accounts well for many features in the experimental data, especially those which remained a puzzle in the earlier work of Gold and Van Schyndel. Experimental ℊc values are given for the first time for most of the extremal orbits on the lead Fermi surface and for high-symmetry directions of the magnetic field. Indeed these are the most detailed data reported for any polyvalent metal. The ℊc factors for the different orbits and field directions are found to span the range from 0.56 to 1.147. These large net deviations from the free-electron value ℊ₀ = 2.0023 are consequences of the strong spin-orbit and electron-phonon interactions, and an attempt has been made to separate these two contributions to the ℊ-shifts. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Electron-phonon interactions (EPIs) are ubiquitous in condensed matter physics and materials science. They are crucial for understanding numerous phenomena, including conventional superconductivity, charge-transport and, most pertinent for this thesis, polaron formation. A polaron is a charge carrier (electron or hole) dressed with a “cloud” of phonons. The polaronic quasiparticle may have vastly different ground- and excited-state properties from that of the bare, constituent charge carrier. While polarons are well-studied and largely understood in canonical model Hamiltonians, recent advances have made it possible to study more complex, fully ab initio systems. Here, the numerically exact methods which are available for some model systems become much more challenging to apply, so accurate approximate methods are a necessity. In this dissertation, we present several advancements in approximate but accurate methods for different polaronic problems and polaron observables. With respect to polaron dynamics, we focus on low-scaling methods to produce wave vector-dependent single-particle spectral function. We present a thorough study of the accuracy of the second- and fourth-order cumulant expansions (CE) of the electronic Green’s function by comparing them against numerically-exact reference data for the one-dimensional Holstein model. We find that the second-order CE is accurate at zero electronic-momentum across a wide range of temperatures, while for non-zero electronic momenta, the CE is only accurate at high-temperatures. The fourth-order cumulant expansion improves on the dynamics at short times and can improve the spectra; however, it can also introduce non-physical divergences and negative spectral weight. The second-order cumulant expansion is thus a useful tool for determining spectral functions in some instances. However, increasing the order of the CE introduces pathologies that may persist at arbitrarily high-order. As an alternate approach to improving the CE, we introduce a new self-consistent cumulant expansion (SC-CE) which remedies many of the deficits of the CE. We compare the results for this new approximation against those from the second-order cumulant expansion as well as reference data for the one-dimensional Holstein model. Unlike the CE, the SC-CE can produce accurate spectra across the entire Brillouin-zone, and captures non-perturbative features excellently. The trade-off for this increased accuracy is the introduction of some degree of negative spectral-weight and the potential for rapid divergences in time in some instances. We find that these problems can be minimized, but not completely eliminated in the thermodynamic limit and in more realistic cases where phonon dispersion exists. We also demonstrate how the SC-CE fits into the greater scheme of Green’s function methods which approximate the self-energy non-diagrammatically as has recently been proposed by Pandey and Littlewood, and we note the potential applications of the SC-CE both in ab initio polaron problems and in general many-body problems. We finally consider a new method to determine the ground-state structure of the polaron in ab initio materials, a topic which has only recently appeared in the literature. We present a new all-coupling variational method based on the Nagy-Markoš variational ansatz for the Fröhlich model. The ansatz is a projected unitary transform which naturally interpolates between the weak-coupling (Lee-Low-Pines) ansatz and the strong-coupling adiabatic ansatz by modulating the momentum conservation of the electron-phonon scattering processes. We demonstrate our ab initio Nagy-Markoš ansatz on the Holstein model and the Fröhlich model, and show that it always improves upon the better of the weak or strong coupling result. We consider the ab initio case of lithium fluoride (LiF), and find that the ansatz provides accurate polaron binding energies for both the hole-polaron and the electron-polaron which are classical cases of small and large polarons, respectively. We note how our flexible variational ansatz is an ideal starting point for perturbative energy corrections and cumulant Green’s function methods. Future developments and applications of the efficient methodologies presented in this dissertation may enable quantitative calculations of polarons in large-intermediately coupled ab initio systems, such as the lead-halide perovskites and other systems where it has hitherto been difficult to fully understand the effects of the electron-phonon interactions.

In this thesis, I explore dissipative quantum dynamics of several prototypical model systems via various approaches, ranging from approximate to numerically exact schemes. In particular, in the realm of the approximate I explore the accuracy of Padé–resummed master equations and the fewest switches surface hopping (FSSH) algorithm for the spin–boson model, and non-crossing approximations (NCA) for the Anderson–Holstein model. Next, I develop new and exact Monte Carlo approaches and test them on the spin–boson model. I propose well–defined criteria for assessing the accuracy of Padé-resummed quantum master equations, which correctly demarcate the regions of parameter space where the Padé approximation is reliable. I continue the investigation of spin–boson dynamics by benchmark comparisons of the semiclassical FSSH algorithm to exact dynamics over a wide range of parameters. Despite small deviations from golden-rule scaling in the Marcus regime, standard surface hopping algorithm is found to be accurate over a large portion of parameter space. The inclusion of decoherence corrections via the augmented FSSH algorithm improves the accuracy of dynamical behavior compared to exact simulations, but the effects are generally not dramatic for the cases I consider. Next, I introduce new methods for numerically exact real-time simulation based on real-time diagrammatic Quantum Monte Carlo (dQMC) and the inchworm algorithm. These methods optimally recycle Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. In the context of the spin–boson model, I formulate the inchworm expansion in two distinct ways: the first with respect to an expansion in the system–bath coupling and the second as an expansion in the diabatic coupling. In addition, a cumulant version of the inchworm Monte Carlo method is motivated by the latter expansion, which allows for further suppression of the growth of the sign error. I provide a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each. Finally, I investigate the dynamical interplay between the electron–electron interaction and the electron–phonon coupling within the Anderson–Holstein model via two complementary NCAs: the first is constructed around the weak-coupling limit and the second around the polaron limit. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. I find the two NCAs disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The complementary frameworks used here pave the way for numerically exact methods based on inchworm dQMC algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.

Spin and charge density fluctuations are important excitations in the strongly correlated systems, especially in the recently discovered high temperature superconductors. Several different theories on high temperature superconductors have been proposed based on spin fluctuations. However, experiments have also shown the existence of strong charge fluctuations. It is, therefore, desirable to investigate the physical consequences of the coexistence of strong spin and charge density fluctuations. As a first step toward a full understanding of both spin and charge excitations, a self-consistent theory is established. In this self-consistent theory, there are three important quantities, the spin susceptibility, the charge susceptibility, and the phonon Green's function. These three quantities are coupled together by the electron-phonon and phonon-spin fluctuation interactions. The phonon-spin fluctuation interaction is derived by making use of the spin-orbital coupling. For a strongly correlated system, the spin and charge density excitations have to be considered self-consistently. They are intimately related. The effects of antiparamagnons on phonons are also investigated. Antiparamagnons can have dramatic effects on phononic properties. It is found that new modes are formed in the presence of antiferromagnetic spin fluctuations. The de Haas-van Alphen effect in marginal and nearly antiferromagnetic Fermi liquids is studied. It is found that the de Haas-van Alphen frequency is unaffected by the anomalous response functions of the marginal and nearly antiferromagnetic Fermi liquids due to the absence of real parts of self-energies on the imaginary frequency axis. / Graduation date: 1993

Transport properties of the two-dimensional electron gas (2DEG) in high magnetic fields are used to investigate scattering processes affecting the resistivity of GaAs-GaAlAs and GaInAs-InP heterojunctions and quantum wells: especially coupling of electrons to acoustic and optic phonons; and transitions between electric subbands. The experiments fall into two groups: A systematic study of magnetophonon resonance (MPR) between 30K and 300K. Resonance positions indicate a coupling substantially below the LO phonon energy, expected from 3D measurements. GaAs-GaAlAs hetero junctions show amplitudes varying smoothly with electron density (n_s) and closely related to the 4K mobility. On rotation in magnetic field they decrease rapidly as the resonance position returns to the LO value. In modulation doped structures the damping factor is determined by remote impurity scattering. As n_s is increased in GaInAs-InP the coupling frequency decreases dramatically from the GaAs-like LO at 272cm^-1 to the InAs-like TO at 226cm^-1. At higher electric fields the 'normal' MPR maxima invert, starting at low magnetic fields, to form 'hot electron' MPR minima, with maximum amplitude at ~60K. This is the first direct observation of HEMPR in 2D and is explained in a diffusion picture. At lower electric fields, additional resonances are identified with resonant cooling by inter-subband scattering. Comparisons are made with calculations and explanations sought including consideration of interface phonons; coupled plasmon-phonon modes; and shifts of the resonance positions due to the shape of the density of states. Low temperature magnetoresistance measurements in GaAs-GaAlAs heterojunctions with more than one occupied electric subband. Shubnikov-de Haas oscillations in perpendicular magnetic fields contain non-additive terms at electron temperatures > 2K where acoustic phonon mediated inter-subband scattering is comparable to intra-subband scattering. Subband separations and greatly enhanced g-factors [largest for electrons in the upper subband ] are deduced from the oscillations. Damping of the oscillations in field, gives values for quantum lifetimes (τ_s), much smaller than τ_tʼ, deduced from mobility. With two subbands occupied τ_s is always largest for the upper subband, while relative sizes of τ_t depend on sample quality. Study of electron energy loss rates, from thermal damping of the oscillations, shows enhancement in the region kT_e ~ ħω_cʼ, which is evidence for cyclotron phonon emission. Depopulating subbands in parallel fields causes the resistance to drop, by up to 60%, due to suppression of inter-subband scattering. Systematic studies show this scattering rate is independent of n_s.

Thesis (Ph.D.)--Ohio University, August, 2008. / Title from PDF t.p. Includes bibliographical references.

In this thesis I present contributions to the development, analysis and application of tensor network state methods for numerically exact quantum dynamics in one and two-dimensional lattice systems. The setting of numerically exact quantum dynamics is introduced in Chapter 2. This includes a discussion of exact diagonalization approaches and massively parallel implementations thereof as well as a brief introduction of tensor network states. In Chapter 3, I perform a detailed analysis of the performance of n-ary tree tensor network states for simulating the dynamics of two-dimensional lattices. This constitutes the first application of this class of tensor network to dynamics in two spatial dimensions, a long-standing challenge, and the method is found to perform on par with existing state-of-the-art approaches. Chapter 4 showcases the efficacy of a novel tensor network format I developed, tailored to electron-phonon coupled problems in their single-electron sector, through an application to the Holstein model. The applicability of the approach to a broad range of parameters of the model allows to reveal the strong influence of the spread of the electron distribution on the initial state of the phonons at the site where the electron is introduced, for which a simple physical picture is offered. I depart from method development in Chapter 5 and analyse the prospects of using tensor network states evolved using the time-dependent variational principle as an approximate approach to determine asymptotic transport properties with a finite, moderate computational effort. The method is shown to not yield the correct asymptotics in a clean, non-integrable system and can thus not be expected to work in generic systems, outside of finely tuned parameter regimes of certain models. Chapters 6 and 7 are concerned with studies of spin transport in long-range interacting systems using tensor network state methods. For the clean case, discussed in Chapter 6, we find that for sufficiently short-ranged interactions, the spreading of the bulk of the excitation is diffusive and thus dominated by the local part of the interaction, while the tail of the excitation decays with a powerlaw that is twice as large as the powerlaw of the interaction. Similarly, in the disordered case, analysed in Chapter 7, we find subdiffusive transport of spin and sub-linear growth of entanglement entropy. This behaviour is in agreement with the behaviour of systems with local interactions at intermediate disorder strength, but provides evidence against the phenomelogical Griffith picture of rare, strongly disordered insulating regions. We generalize the latter to long-ranged interactions and show that it predicts to diffusion, in contrast to the local case where it results in subdiffusive behaviour.

Lo Loc Ping = 多體量子系統問題 / 盧樂平. / Thesis submitted in: October 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 168-171). / Text in English; abstracts in English and Chinese. / Lo Loc Ping = Duo ti liang zi xi tong wen ti / Lu Leping. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgment --- p.iii / Chapter I --- Computational Quantum Mechanics and Its Applications 電算量子力學及其應用 --- p.1 / Chapter 1 --- An Overview of Quantum Mechanics and Some Important Tools of Theory --- p.2 / Chapter 1.1 --- The Schrodinger Equation --- p.2 / Chapter 1.2 --- The Variational Method --- p.4 / Chapter 1.2.1 --- Rayleigh-Ritz Approach --- p.4 / Chapter 1.2.2 --- Linear Variation --- p.5 / Chapter 2 --- Theoretical Methodology of Electronic Structures: Ab Initio Molecular Orbital Theory --- p.7 / Chapter 2.1 --- The Molecular Hamiltonian --- p.7 / Chapter 2.2 --- Hartree Description and Linear Combination of Atomic Orbitals Expan- sion --- p.8 / Chapter 2.3 --- Slater Determinant and the Pauli Exclusion Principle --- p.9 / Chapter 2.4 --- The Expansion of E in Terms of Integrals over MOs --- p.11 / Chapter 2.5 --- Derivation of the Hartree´ؤFock Equations --- p.15 / Chapter 2.6 --- The Self-Consistent Field Calculation --- p.18 / Chapter 2.7 --- Koopmans' Theorem --- p.19 / Chapter 2.8 --- Orbital and the Total SCF Electronic Energy --- p.20 / Chapter 2.9 --- AO Basic Sets --- p.21 / Chapter 2.9.1 --- Slater-Type Orbitals --- p.21 / Chapter 2.9.2 --- Gaussian Functions --- p.22 / Chapter 2.10 --- The Hartree-Fock Limit --- p.23 / Chapter 2.11 --- Electron Correlation --- p.23 / Chapter 2.11.1 --- Weakness in the Single Determinant Model --- p.23 / Chapter 2.11.2 --- Configuration Interaction --- p.24 / Chapter 2.11.3 --- The Coupled-Cluster Method --- p.25 / Chapter 2.11.4 --- Density Functional Theory --- p.26 / Chapter 2.12 --- Frontier Orbitals --- p.31 / Chapter 3 --- Theoretical Investigation of the Interaction between Metal and Tris(8- hydroxyquinoline) aluminum in Organic Light Emitting Diodes --- p.32 / Chapter 3.1 --- Organic Light Emitting Diodes and Tris(8-hydro-xyquinoline) aluminum --- p.32 / Chapter 3.2 --- Computational Methodology --- p.33 / Chapter 3.3 --- Alq3 --- p.34 / Chapter 3.3.1 --- Molecular Structure --- p.34 / Chapter 3.3.2 --- Electronic Structure --- p.36 / Chapter 3.3.3 --- Transition and Relaxation Energies --- p.44 / Chapter 3.3.4 --- Interactions with Metals --- p.45 / Chapter 3.4 --- "Li-Alq3, Na-Alq3 and K-Alq3 Complexes" --- p.46 / Chapter 3.4.1 --- Molecular Structure --- p.46 / Chapter 3.4.2 --- Ground-State Electronic Structure --- p.55 / Chapter 3.4.3 --- Transition and Relaxation Energies --- p.67 / Chapter 3.5 --- "Be-Alq3, Mg´ؤAlq3 and Ca´ؤAlq3 Complexes" --- p.68 / Chapter 3.5.1 --- Molecular Structure --- p.68 / Chapter 3.5.2 --- Ground-State Electronic Structure --- p.76 / Chapter 3.5.3 --- Transition and Relaxation Energies --- p.87 / Chapter 3.6 --- "B-Alq3, Al-Alq3 and Ga-Alq3 Complexes" --- p.87 / Chapter 3.6.1 --- Molecular Structure --- p.87 / Chapter 3.6.2 --- Ground-State Electronic Structure --- p.95 / Chapter 3.6.3 --- Transition and Relaxation Energies --- p.106 / Chapter II --- Analytical Studies of Polarons and the Electron-Phonon Interaction 極子與電子一聲子相互作用的 解析研究 --- p.107 / Chapter 4 --- Optimal Coupled-Cluster Approximation of the Ground-State Energy of the E× (α1 + α1) Jahn-Teller System --- p.108 / Chapter 4.1 --- The Jahn-Teller Effect --- p.108 / Chapter 4.2 --- Approximation in the Coupled-Cluster Method and the Jahn-Teller Hamiltonian --- p.110 / Chapter 4.3 --- Variational Coupled-Cluster Approximation --- p.112 / Chapter 4.3.1 --- The Zeroth Level --- p.113 / Chapter 4.3.2 --- The First Level --- p.113 / Chapter 4.3.3 --- The Second and the Third Levels --- p.114 / Chapter 4.4 --- An 'Optimal' Hamiltonian --- p.115 / Chapter 4.5 --- Treatment for the k> 1 Case --- p.117 / Chapter 4.6 --- Energies and Other Physical Phenomena --- p.118 / Chapter 5 --- Small-to-Large Ground-State Polaron Crossover in One-Dimension Extended E×e Jahn-Teller System Using Variational Coupled-Cluster Approximation --- p.134 / Chapter 5.1 --- Polaron Formation --- p.134 / Chapter 5.2 --- Model Hamiltonian and the MLF Transformation --- p.135 / Chapter 5.3 --- Variatonal Coupled-Cluster Approximation --- p.137 / Chapter 5.3.1 --- Zeorth Level --- p.139 / Chapter 5.3.2 --- First Level --- p.139 / Chapter 5.3.3 --- Second Level --- p.142 / Chapter 5.4 --- Energies and Static Correlation Functions --- p.142 / Chapter 5.5 --- Approximate Form of the MLF Transformation for K = 0 --- p.153 / Chapter 5.5.1 --- Zeroth Level --- p.154 / Chapter 5.5.2 --- First Level --- p.155 / Chapter 5.5.3 --- Second Level --- p.156 / Chapter 5.5.4 --- Energies and Static Correlation Functions --- p.157 / Chapter 5.6 --- Synopsis --- p.167 / Bibliography --- p.171

Yeung Man Yi = 多體量子系統問題 / 楊曼儀. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves [247-249]). / Text in English; abstracts in English and Chinese. / Yeung Man Yi = Duo ti liang zi xi tong wen ti / Yang Manyi. / Abstract --- p.i / Acknowledgment --- p.iii / Chapter I --- Computational Quantum Mechanics and Its Applications / 電算量子力學及其應用 --- p.1 / Chapter 1 --- Theoretical Methodology of Electronic Structures: Ab Initio Molecular Orbital Theory --- p.2 / Chapter 1.1 --- Molecular Hamiltonian --- p.2 / Chapter 1.2 --- Hartree Products --- p.5 / Chapter 1.3 --- Slater Determinants and Pauli Exclusion Principle --- p.6 / Chapter 1.4 --- Expansion of Total Electronic Energy in terms of Integrals over MOs --- p.8 / Chapter 1.5 --- Derivation of the Hartree-Fock Equations --- p.11 / Chapter 1.6 --- Orbital Energies and the Koopmans' Theorem --- p.14 / Chapter 1.7 --- AO Basic Sets --- p.17 / Chapter 1.7.1 --- Slater-Type Orbitals --- p.18 / Chapter 1.7.2 --- Gaussian Functions --- p.18 / Chapter 1.8 --- Self-Consistent Field Calculation --- p.19 / Chapter 1.9 --- Hartree-Fock Limit --- p.20 / Chapter 1.10 --- Electron Correlation --- p.20 / Chapter 1.10.1 --- Configuration Interaction --- p.20 / Chapter 1.10.2 --- Density Functional Theory --- p.21 / Chapter 2 --- Theoretical Investigation of Organic Light Emitting Molecules --- p.29 / Chapter 2.1 --- Introduction --- p.29 / Chapter 2.2 --- Methodology --- p.31 / Chapter 2.2.1 --- Theoretical Methodology --- p.31 / Chapter 2.2.2 --- Computational Methodology --- p.35 / Chapter 2.3 --- ADN series --- p.35 / Chapter 2.3.1 --- Molecular Structure --- p.36 / Chapter 2.3.2 --- Electronic Structure --- p.49 / Chapter 2.3.3 --- Absorption and Emission Energy --- p.55 / Chapter 2.3.4 --- Reorganization Energy --- p.56 / Chapter 2.3.5 --- Mobility --- p.57 / Chapter 2.3.6 --- Summary on ADN series --- p.66 / Chapter 2.4 --- XOT series --- p.67 / Chapter 2.4.1 --- Molecular Structure --- p.68 / Chapter 2.4.2 --- Electronic Structure --- p.89 / Chapter 2.4.3 --- Absorption and Emission Energy --- p.96 / Chapter 2.4.4 --- Reorganization Energy and Mobility --- p.98 / Chapter 2.4.5 --- Summary on XOT series --- p.100 / Chapter 2.5 --- KPA series --- p.102 / Chapter 2.5.1 --- Molecular Structure --- p.102 / Chapter 2.5.2 --- Electronic Structure --- p.123 / Chapter 2.5.3 --- Absorption and Emission Energy --- p.131 / Chapter 2.5.4 --- Reorganization Energy and Mobility --- p.131 / Chapter 2.5.5 --- Summary on KPA series --- p.133 / Chapter 2.6 --- NPA series --- p.136 / Chapter 2.6.1 --- Molecular Structure --- p.136 / Chapter 2.6.2 --- Electronic Structure --- p.160 / Chapter 2.6.3 --- Absorption and Emission Energy --- p.166 / Chapter 2.6.4 --- Reorganization Energy and Mobility --- p.167 / Chapter 2.6.5 --- Summary on NPA series --- p.169 / Chapter II --- Analytical Studies of Polarons and the Electron-Phonon Interaction / 極子與電子一聲子相互作用的解析研究 --- p.172 / Chapter 3 --- Study on Holstein Model Using Variational Approximation --- p.173 / Chapter 3.1 --- Holstein Hamiltonian --- p.173 / Chapter 3.2 --- Variational Transformation --- p.175 / Chapter 3.2.1 --- Lang-Firsov Transformation --- p.175 / Chapter 3.2.2 --- Squeezing Transformation --- p.177 / Chapter 3.3 --- Energy and Static Correlation Functions --- p.179 / Chapter 4 --- Study on Holstein Model Using Coupled-Cluster Method --- p.193 / Chapter 4.1 --- Approximation in the Coupled-Cluster Method --- p.193 / Chapter 4.2 --- Approach 1 --- p.195 / Chapter 4.2.1 --- The Zeroth and the First Levels --- p.195 / Chapter 4.2.2 --- Energies and Static Correlation Functions --- p.196 / Chapter 4.3 --- Approach 2 --- p.206 / Chapter 4.3.1 --- The Zeroth and the First Levels --- p.206 / Chapter 4.3.2 --- Energies and Static Correlation Functions --- p.210 / Chapter 4.4 --- Approach 3 --- p.225 / Chapter 4.4.1 --- The Zeroth and the First Levels --- p.226 / Chapter 4.4.2 --- Energies and Static Correlation Functions --- p.228 / Chapter 4.5 --- Comparison with the Variational Method --- p.243