The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a |omega| dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln omega divergence found in the low frequency behaviour of the T=0 dynamic susceptibility.The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a |omega| dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln omega divergence found in the low frequency behaviour of the T=0 dynamic susceptibility.

Jan 1, 199911 citations

On the normal phase of 2D Fermi liquid with weak attraction between particles

V. P. Gusynin, В. М. Локтев, Igor A. Shovkovy

Proceeding from the simplest field theoretical model of 2D metal, the normal phase Green functions of the weakly interacting fermions and the order parameter fluctuations (responsible for the attraction between fermions) are obtained. It is shown that taking into consideration the fluctuations mentioned leads to a considerable reduction of the fermion wave function renormalization constant (quasiparticle weight) as well as to a linear dependence of the quasiparticle damping on the temperature. A general dependence of 2D Fermi liquid properties on the fermion density is discussed. The relevance of the proposed model to the marginal behavior of the Fermi liquid of high-- $T_c$ superconductors, in particular, to their linear temperature dependence of the resistivity is indicated.Proceeding from the simplest field theoretical model of 2D metal, the normal phase Green functions of the weakly interacting fermions and the order parameter fluctuations (responsible for the attraction between fermions) are obtained. It is shown that taking into consideration the fluctuations mentioned leads to a considerable reduction of the fermion wave function renormalization constant (quasiparticle weight) as well as to a linear dependence of the quasiparticle damping on the temperature. A general dependence of 2D Fermi liquid properties on the fermion density is discussed. The relevance of the proposed model to the marginal behavior of the Fermi liquid of high--$T_c$ superconductors, in particular, to their linear temperature dependence of the resistivity is indicated.

arXiv:cond-mat/9508076Aug 18, 19950 citations

Toward a microscopic analysis of the marginal fermi liquid

M. Crişan, Liviu Tătaru

Journal of SuperconductivityOct 1, 19933 citations

Model of a Two-Dimensional Marginal Fermi Liquid Superconductor

Yu-Liang Liu, Tai Kai Ng

In this paper we study a model of an $s$ -wave marginal Fermi liquid superconductor in two dimensions. Besides the usual Bardeen-Cooper-Schrieffer (BCS) point attractive interaction, the fermions in our system also interact via a long-range repulsive interaction $v(q){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}g}_{D}/{q}^{2}$ . We find that although superconductivity is not destroyed by the long-ranged repulsive interaction (demonstrated by the response to electromagnetic magnetic fields), the BCS pairing function ${\ensuremath{\Delta}}_{\mathrm{BCS}}$ is strongly suppressed, resulting in a power-law correlation $〈{\ensuremath{\Delta}}_{\mathrm{BCS}}(\stackrel{\ensuremath{\rightarrow}}{x}){\ensuremath{\Delta}}_{\mathrm{BCS}}(0)〉\ensuremath{\sim}|\stackrel{\ensuremath{\rightarrow}}{x}{|}^{\ensuremath{-}2\ensuremath{\gamma}}$. This observation is explained within a general picture of the marginal Fermi liquid.In this paper we study a model of an $s$-wave marginal Fermi liquid superconductor in two dimensions. Besides the usual Bardeen-Cooper-Schrieffer (BCS) point attractive interaction, the fermions in our system also interact via a long-range repulsive interaction $v(q){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}g}_{D}/{q}^{2}$. We find that although superconductivity is not destroyed by the long-ranged repulsive interaction (demonstrated by the response to electromagnetic magnetic fields), the BCS pairing function ${\ensuremath{\Delta}}_{\mathrm{BCS}}$ is strongly suppressed, resulting in a power-law correlation $〈{\ensuremath{\Delta}}_{\mathrm{BCS}}(\stackrel{\ensuremath{\rightarrow}}{x}){\ensuremath{\Delta}}_{\mathrm{BCS}}(0)〉\ensuremath{\sim}|\stackrel{\ensuremath{\rightarrow}}{x}{|}^{\ensuremath{-}2\ensuremath{\gamma}}$. This observation is explained within a general picture of the marginal Fermi liquid.

Physical Review LettersDec 27, 19999 citations

Towards a theory of the marginal fermi- liquid state

C. M. Varma

Journal of Physics and Chemistry of SolidsOct 1, 19939 citations

T_c

superconductors, in particular, to their linear temperature dependence of the resistivity is indicated.

In this paper we study a model of an

s

-wave marginal Fermi liquid superconductor in two dimensions. Besides the usual Bardeen-Cooper-Schrieffer (BCS) point attractive interaction, the fermions in our system also interact via a long-range repulsive interaction

v(q){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}g}_{D}/{q}^{2}

. We find that although superconductivity is not destroyed by the long-ranged repulsive interaction (demonstrated by the response to electromagnetic magnetic fields), the BCS pairing function ${\ensuremath{\Delta}}_{\mathrm{BCS}}$ is strongly suppressed, resulting in a power-law correlation $〈{\ensuremath{\Delta}}_{\mathrm{BCS}}(\stackrel{\ensuremath{\rightarrow}}{x}){\ensuremath{\Delta}}_{\mathrm{BCS}}(0)〉\ensuremath{\sim}|\stackrel{\ensuremath{\rightarrow}}{x}{|}^{\ensuremath{-}2\ensuremath{\gamma}}$. This observation is explained within a general picture of the marginal Fermi liquid.