Related papers: Fermi Liquids and the Luttinger Integral
Luttinger semimetals have quadratic band crossings at the Brillouin zone-center in three spatial dimensions. Coulomb interactions in a model that describes these systems stabilize a non-trivial fixed point associated with a non-Fermi liquid…
The Kondo-Heisenberg model is used for a microscopic demonstration of existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. I use a…
In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system…
Unitary limit for model point scatterers in graphene is known to reveal low-energy resonances. The same limit could be achieved from hybridization of band electrons with the localized impurity level positioned in the vicinity of the Fermi…
Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include…
A Fermi Liquid theory is developed for the persistent current past a side coupled quantum dot yielding analytical predictions for the behavior of the first two harmonics of the persistent current as a function of applied magnetic flux. The…
We consider a resonant level coupled to a chiral Luttinger liquid which can be realized, e.g., at a fractional quantum Hall edge. We study the dependence of the occupation probability n of the level on its energy \epsilon for various values…
We present numerical evidence for a paradigm in one-dimensional interacting fermion systems, whose phenomenology has traits of both Luttinger liquids and Fermi liquids. This state, dubbed a quasi-Fermi liquid, possesses a discontinuity in…
In this paper, we consider analytically the density evolution of a spinless Fermi liquid with a nonlinear dispersion relation into which one particle is injected. The interaction is point-like and the temperature is zero. We obtain a…
We consider a model of an Anderson impurity embedded in a $d_{x^2-y^2}$-wave superconducting state to describe the low-energy excitations of cuprate superconductors doped with a small amount of magnetic impurities. Due to the Dirac-like…
We consider in depth the applicability of the Wiedemann-Franz (WF) law, namely that the electronic thermal conductivity ($\kappa$) is proportional to the product of the absolute temperature ($T$) and the electrical conductivity ($\sigma$)…
We investigate the approach to the quantum critical point of a Pomeranchuk instability from the symmetric, disordered side of the phase diagram. In the low-temperature limit, a Fermi liquid description of the metal is possible and becomes…
We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landau's theory one can define a fermion excitation renormalized by interaction and show…
The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reaveals that the Luttinger liquid spin susceptibility…
We consider an electron gas, both in two (2D) and three (3D) dimensions, interacting with quenched impurities and phonons within leading order finite-temperature many body perturbation theories, calculating the electron self-energies,…
The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the metal often has different shapes in the states well away from…
Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale $T_{\text{FL}}$ is found to be surprisingly small. In this Letter, we study the simplest…
We reformulate the Tomonaga--Luttinger liquid theory for quasi-one-dimensional Fermion systems with many subbands across the Fermi energy. Our theory enables us to obtain a rigorous expression of the local density of states (LDOS) for…
This chapter reviews the theoretical description of interacting fermions in one dimension. The Luttinger liquid concept is elucidated using the Tomonaga-Luttinger model as well as integrable lattice models. Weakly coupled chains and…
We argue that a class of strongly spin-orbit coupled materials, including some pyrochlore iridates and the inverted band gap semiconductor HgTe, may be described by a minimal model consisting of the Luttinger Hamiltonian supplemented by…