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Physical review. B, Condensed matter

Anomalous behavior of a Fermi system interacting with a bosonic critical mode

M. Crişan, Liviu Tătaru

Published Aug 1, 1996• 3 citations
Publisher

Abstract

We show that a three-dimensional Fermi liquid with a gap in the electron-hole energy excitations has an anomalous behavior if it interacts with a bosonic critical mode. Such a model can be obtained from the Kondo-Hubbard Hamiltonian which describes a strong correlated Fermi liquid with ferromagnetic ground state. The model can be interesting for the anomalous behavior of oxide superconductors and heavy fermion superconductors which, in the normal state, present a strong deviation from the Landau theory of the Fermi liquids. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.3597

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We show that a three-dimensional Fermi liquid with a gap in the electron-hole energy excitations has an anomalous behavior if it interacts with a bosonic critical mode. Such a model can be obtained from the Kondo-Hubbard Hamiltonian which describes a strong correlated Fermi liquid with ferromagnetic ground state. The model can be interesting for the anomalous behavior of oxide superconductors and heavy fermion superconductors which, in the normal state, present a strong deviation from the Landau theory of the Fermi liquids. \textcopyright{} 1996 The American Physical Society.
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A model of two interacting one-dimensional fermion systems (``Luttinger liquids'') coupled by single-particle hopping is investigated. Bosonization allows a number of exact statements to be made. In particular, for forward scattering only, the model contains two massless boson sectors and an Ising-type critical sector. For general repulsive interactions, there is a spin excitation gap and either d-type pairing or orbital antiferromagnetic fluctuations dominate. It is argued that the same behavior is also found for strong interactions. A possible scenario for the crossover to a Fermi liquid in a many-chain system is discussed. \textcopyright{} 1996 The American Physical Society.
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A systematic study of optical and transport properties of the Hubbard model, based on the Metzner-Vollhardt dynamical mean-field approximation, is reviewed. This model shows interesting anomalous properties that are, in our opinion, ubiquitous to single-band strongly correlated systems (for all spatial dimensions greater than one) and also compare qualitatively with many anomalous transport features of the high-T c cuprates. This anomalous behaviour of the normal-state properties is traced to a ‘collective single-band Kondo effect’, in which a quasiparticle resonance forms at the Fermi level as the temperature is lowered, ultimately yielding a strongly renormalized Fermi liquid at zero temperature.
The ground state of the Hubbard model is studied within the constrained Hilbert space where no order parameter exists.The self-energy of electrons is decomposed into the single-site and multisite self-energies.The calculation of the single-site self-energy is mapped to a problem of self-consistently determining and solving the Anderson model.When an electron reservoir is explicitly considered, it is proved that the single-site self-energy is that of a normal Fermi liquid even if the multisite self-energy is anomalous.Thus, the ground state is a normal Fermi liquid in the supreme single-site approximation (S 3 A).In the strong-coupling regime, the Fermi liquid is stabilized by the Kondo effect in the S 3 A and is further stabilized by the Fock-type term of the superexchange interaction or the resonating-valence-bond (RVB) mechanism beyond the S 3 A. The stabilized Fermi liquid is frustrated as much as an RVB spin liquid in the Heisenberg model.It is a relevant unperturbed state that can be used to study a normal or anomalous Fermi liquid and an ordered state in the whole Hilbert space by Kondo lattice theory.Even if higher-order multisite terms than the Fock-type term are considered, the ground state cannot be a Mott insulator.It can be merely a gapless semiconductor even if the multisite self-energy is so anomalous that it is divergent at the chemical potential.A Mott insulator is only possible as a high temperature phase.