We carefully revisit the electron-boson scattering problem, going beyond weak-coupling expansions and popular semiclassical treatments. By providing numerically exact results valid at finite temperatures, we demonstrate the existence of a broad regime of electron-boson scattering where quantum localization processes become relevant despite the absence of extrinsic disorder. Localization in the Anderson sense is caused by the dynamical randomness resulting from a large thermal boson population, being, however, effective only at transient times before diffusion can set in. Compelling evidence of this transient localization phenomenon is provided by the observation of a distinctive displaced Drude peak in the optical absorption and the ensuing suppression of conductivity. Our findings identify a general route for anomalous metallic behavior that can broadly apply in interacting quantum matter.
We carefully revisit the electron-boson scattering problem, going beyond weak-coupling expansions and popular semiclassical treatments. By providing numerically exact results valid at finite temperatures, we demonstrate the existence of a broad regime of electron-boson scattering where quantum localization processes become relevant despite the absence of extrinsic disorder. Localization in the Anderson sense is caused by the dynamical randomness resulting from a large thermal boson population, being, however, effective only at transient times before diffusion can set in. Compelling evidence of this transient localization phenomenon is provided by the observation of a distinctive displaced Drude peak in the optical absorption and the ensuing suppression of conductivity. Our findings identify a general route for anomalous metallic behavior that can broadly apply in interacting quantum matter.
Scattering by slowly fluctuating degrees of freedom can cause a transient localization of the current-carrying electrons in metals, driving the system away from normal metallic behavior. We illustrate and characterize this general phenomenon by studying how signatures of localization emerge in the optical conductivity of electrons interacting with slow bosonic fluctuations. The buildup of quantum localization corrections manifests itself in the emergence of a displaced Drude peak (DDP), whose existence strongly alters the low frequency optical response and suppresses the d.c. conductivity. We find that many-body renormalization of the fluctuating field at metallic densities considerably enhances electron localization and the ensuing DDP phenomenon in comparison with the well-studied low concentration limit. Our results are compatible with the frequent observation of DDPs in electronic systems where slowly fluctuating degrees of freedom couple significantly to the charge carriers.
Scattering by slowly fluctuating degrees of freedom can cause a transient localization of the current-carrying electrons in metals, driving the system away from normal metallic behavior. We illustrate and characterize this general phenomenon by studying how signatures of localization emerge in the optical conductivity of electrons interacting with slow bosonic fluctuations. The buildup of quantum localization corrections manifests itself in the emergence of a displaced Drude peak (DDP), whose existence strongly alters the low frequency optical response and suppresses the d.c. conductivity. We find that for sufficiently strong interactions, many-body renormalization of the fluctuating field induced at metallic densities enhances electron localization and the ensuing DDP phenomenon in comparison with the well-studied low concentration limit. Our results are compatible with the frequent observation of DDPs in electronic systems where slowly fluctuating degrees of freedom couple significantly to the charge carriers.
Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important. The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder. The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.
In the absence of frustration, interacting bosons in their ground state in one or two dimensions exist either in the superfluid or insulating phases. Superfluidity corresponds to frictionless flow of the matter field, and in optical conductivity is revealed through a distinct δ-functional peak at zero frequency with the amplitude known as the Drude weight. This characteristic low-frequency feature is instead absent in insulating phases, defined by zero static optical conductivity. Here we demonstrate that bosonic particles in disordered one dimensional chains can also exist in a conducting, non-superfluid, phase when their hopping is of the dipolar type, often viewed as short-ranged in one dimension. This phase is characterized by finite static optical conductivity, followed by a broad anti-Drude peak at finite frequencies. Off-diagonal correlations are also unconventional: they feature an integrable algebraic decay for arbitrarily large values of disorder. These results do not fit the description of any known quantum phase, and strongly suggest the existence of an unusual conducting state of bosonic matter in the ground state.
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.
A nonequilibrium occupation distribution relaxes towards the Fermi-Dirac distribution due to electron-electron scattering even in finite Fermi systems. The dynamic evolution of this thermalization process assumed to result from an optical excitation is investigated numerically by solving a Boltzmann equation for the carrier populations using a one-dimensional disordered system. We focus on the short-time-scale behavior. The logarithmically long time scale associated with the glassy behavior of interacting electrons in disordered systems is not treated in our investigation. For weak disorder and short range interaction we recover the expected result that the relaxation rate is enhanced by disorder. For sufficiently strong disorder, however, we find an opposite trend due to the reduction of scattering probabilities originating from the strong localization of the single-particle states. Long-range interaction in this regime produces a similar effect. The relaxation rate is found to scale with the interaction strength, however, the interplay between the implicit and the explicit character of the interaction produces an anomalous exponent.