There are two distinct single-particle-like structures associated with dynamic fermionic quantum impurity systems. There are the quasiparticles that provide a description of low-energy excitations in terms of independent effective degrees of freedom. Then there is also the natural orbital basis, associated with the bare electronic degrees of freedom, which provides an economical description of ground-state correlations. This study employs natural orbitals to describe explicitly how bare electrons are dressed to form local Fermi liquid quasiparticles.
There are two distinct single-particle-like structures associated with dynamic fermionic quantum impurity systems. There are the quasiparticles that provide a description of low-energy excitations in terms of independent effective degrees of freedom. Then there is also the natural orbital basis, associated with the bare electronic degrees of freedom, which provides an economical description of ground-state correlations. This study employs natural orbitals to describe explicitly how bare electrons are dressed to form local Fermi liquid quasiparticles.
Conduction electrons interacting with a dynamic impurity can give rise to a local Fermi liquid. The latter has the same low energy spectrum as an ideal Fermi gas containing a static impurity. The Fermi liquids's elementary excitations are however not bare electrons. In the vicinity of the impurity, they are dressed by virtual particle-hole pairs. Here we study this dressing. Among other things, we construct a mode-resolved measure of dressing. To evaluate it in position representation, we have to circumvent the limitations of the Numerical Renormalization Group, which discretizes the conduction band logarithmically. We therefore extend Natural Orbital methods, that successfully characterize the ground state, to describe excitations. We demonstrate that the dressing profile shows nontrivial powerlaw decay at large distances. Our Natural Orbital methodology could lay the foundation for calculating the properties of local Fermi liquid quasiparticles in nontrivial geometries such as disordered hosts or mesoscopic devices.
Low-temperature properties of 3D interacting fermion systems are well described by Landau's theory of Fermi liquids; for reviews see, e.g. [183, 184]. It involves only excitations of the system around the Fermi surface on energy scales small compared to the Fermi energy. Excitations are well described by quasi-particles which are in one-to-one correspondence with the bare particles. The bare-particle interaction does not break the qualitative picture of non-interacting system, but renormalizes the dynamical characteristics (the effective mass and the pair interaction) of quasi-particles. Within the microscopic Green function formalism, the existence of quasi-particles is equivalent to assuming that the self-energy correction Σ( k , ω) is regular (has only short-range contributions in time and space) close to the Fermi surface. The lifetime of quasi-particles τ α(ε k −ε F ) −2 is long enough to consider them as well-defined eigenstates over long time-scales. The momentum occupation number of the bare particles exhibits a sharp discontinuity when crossing the Fermi momentum. The charge and spin degrees of freedom of quasi-particle always travel together. The Landau theory breaks down in 1D systems of interacting fermions which have a very specific Fermi surface consisting of two points ± k F . In such systems, the self-energy Σ( k , ω) no longer possesses the analytic properties required for introducing quasi-particles. In contrast to Fermi liquids, the momentum occupation number of the bare particles in the ground state is continuous at the Fermi momentum. Moreover, the charge and spin excitations are separated.
A model of a Fermi liquid with the fermion condensate (FC) is applied to the consideration of quasiparticle excitations in high-temperature superconductors, in their superconducting and normal states. Within our model the appearance of the fermion condensate presents a quantum phase transition that separates the regions of normal and strongly correlated electron liquids. Beyond the phase transition point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other---fermion condensate localized at the Fermi surface and characterized by almost dispersionless single-particle excitations. In the superconducting state the quasiparticle dispersion in systems with FC can be presented by two straight lines, characterized by effective masses MFC∗ and ML∗, respectively, and intersecting near the binding energy, which is of the order of the superconducting gap. This same quasiparticle picture persists in the normal state, thus manifesting itself over a wide range of temperatures as new energy scales. Arguments are presented that fermion systems with FC have features of a ``quantum protectorate'' [R. B. Laughlin and D. Pines, Proc. Natl. Acad. Sci. U.S.A. 97, 28 (2000); P. W. Anderson, cond-mat/0007185 (unpublished); cond-mat/0007287 (unpublished)].
Many strongly correlated electron systems fall outside the conventional quasiparticle paradigm. Their low-energy fermionic excitations need not be adiabatically connected to the bare electrons or appear as poles of the physical electron single-particle Green's function. This thesis investigates to what extent an effective quasiparticle description can nevertheless survive, and which emergent degrees of freedom provide the appropriate low-energy structure. First, the interaction-driven evolution from a quantum spin Hall insulator to a Mott insulator is studied using the dynamical cluster approximation. Dispersive zeros of the single-particle Green's function emerge near the Mott transition and retain a nontrivial topological character. When symmetry breaking is allowed, a nontopological excitonic insulator is found to intrude between quantum spin Hall and Mott insulators. Encoding both poles and zeros within a low-energy quasiparticle Hamiltonian provides a continuous one-body description of the three phases. On the Mott side, its gap evolution supports interpreting the soft excitonic mode as a bound state of quasiparticle and quasihole excitations tied to the Green's function zeros, rather than to the widely separated Hubbard bands. Second, the intrinsic anomalous Hall conductivity of a topological metal is analyzed within a multiband extension of Landau Fermi-liquid theory. Residual interactions among quasiparticles at the Fermi surface dress the dynamic current vertex and generate corrections to the Berry-curvature contribution obtained from the quasiparticle bands alone. Our result supports recent claims that the correct expressions for topological observables include vertex corrections besides the topological invariants built just upon the Green's function. It also demonstrates that such corrections are naturally accounted for by Landau Fermi-liquid theory. Extracting the relevant ingredients for an effective description of material-relevant correlated systems requires computational tools that remain reliable at low temperatures. To this end, a deterministic strong-coupling impurity solver for dynamical mean-field theory is discussed. By providing static, dynamical, and thermodynamic observables without stochastic sampling, it offers a promising route toward multiorbital and spin-orbit coupled problems where conventional Monte Carlo methods currently struggle. Finally, the auxiliary quasiparticle framework underlying the ghost-Gutzwiller Ansatz is investigated. On a model for correlated quantum spin Hall insulators, we show that the topology of the interacting state is encoded in the auxiliary one-body Hamiltonian. The resulting band-structure reveals topological Hubbard bands whose topological character can be tuned through a finite magnetization. When applied to the single-band t-J model, the same framework yields a fractionalized Fermi liquid (FL*). In this phase, dispersive neutral spinons, with vanishing physical-electron spectral weight, coexist with conventional quasiparticles forming a small hole-like Fermi surface, thus violating Luttinger's theorem. The corresponding temperature--doping phase diagram contains a low-doping FL*, a d-wave superconducting dome, and an overdoped conventional Fermi liquid, thereby reproducing key qualitative features of cuprate phenomenology.
Abstract Dedicated to Bernhard Mühlschlegel on the occasion of his 80th birthday We address the question, whether low lying one‐particle excitations in the Fermi‐liquid phase of highly correlated electron systems can form well defined bands of nearly stable quasiparticles, and comment on features of a universal band picture for these systems. We outline how to derive a description of instabilities to magnetic, charged ordered or superconducting phases, which bears a close analogy to Stoner theory and lends itself to an interpretation in terms of quasiparticle bands and residual interactions at low temperatures. Concepts and problems are illustrated via calculations for some standard models of solid‐state theory using modern many‐body techniques like NRG, NCA and DMFT. Differences to conventional band structure theory are pointed out. We shortly comment on the relevance of these questions to the physics of inhomogeneous systems and small particles.
We study correlated quantum impurity models that undergo a local quantum phase transition (QPT) from a strong coupling, Fermi liquid phase to a non-Fermi liquid phase with a globally doubly degenerate ground state. Our aim is to establish what can be shown exactly about such ``local moment'' (LM) phases, of which the permanent (zero-field) local magnetization is a hallmark, and an order parameter for the QPT. A description of the zero-field LM phase is shown to require two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the single self-energy of standard field theory. Distinct Friedel sum rules for each phase are obtained, via a Luttinger theorem embodied in the vanishing of appropriate Luttinger integrals. By contrast, the standard Luttinger integral is nonzero in the LM phase but found to have universal magnitude. A range of spin susceptibilites are also considered, including that corresponding to the local order parameter, whose exact form is shown to be RPA-like, and to diverge as the QPT is approached. Particular attention is given to the pseudogap Anderson model, including the basic physical picture of the transition, the low-energy behavior of single-particle dynamics, the quantum critical point itself, and the rather subtle effect of an applied local field. A two-level impurity model that undergoes a QPT (``singlet-triplet'') to an underscreened LM phase is also considered, for which we derive on general grounds some key results for the zero-bias conductance in both phases.