Non-Fermi Behavior of the Strongly Correlated Electron Systems

(1) The temperature dependence of the specific heat for a marginal Fermi liquid has been calculated . We showed that the expected T lnT correction is characteristic for the low temperature domain. The high temperature domain has a supplementary correction. The results are in agreement with the non-Fermi behavior of some metallic systems in the low temperature domain. (2) We calculated the self-energy at T = 0 for a two dimensional fermionic system with hyperbolic dispersion. The existence of the saddle points in the energy gives rise to a marginal behavior, a result which has been obtained by numerical calculations. (3) We present a simple demonstration that the two-dimensional fermionic system with the energy εk = kxky has a non-Fermi behavior. The calculation of the wave function renormalization constant Z were performed using the ”poor man’s renormalization” method and we have showed that Z → 0 with the infrared cut-off Λ as Z(Λ) = Λζ where ζ is a constant. (4) The electronic self-energy due to the electron-spin interaction is calculated using the one-loop approximation for the two dimensional system and quasi-two dimensional (anisotropic) model. We analyzed the relevance of the diffusive modes and the temperature dependence of the magnetic correlation length for a possible temperature dependence of the pseudogap. (5) We study the influence of the amplitude fluctuations of a non-Fermi superconductor on the energy spectrum of the two-dimensional Anderson non-Fermi system. The classical fluctuations give a temperature dependence in the pseudogap induced in the fermionic excitations. (6) Using the field-theoretical methods we studied the evolution from BCS description of a non-Fermi superconductor to that of Bose-Einstein condensation (BEC) in one loop approximation. We showed that the repulsive interaction between composite bosons is determined by the exponent α of the Anderson propagator in a two dimensional model. For α 6= 0 the crossover is also continuous and for α = 0 we obtain the case of the Fermi liquid. (7) Using the renormalization group approach proposed by Millis for the itinerant electron systems we calculated the specific heat coefficient γ(T ) for the magnetic fluctuations with susceptibility χ−1 ∼ δα + |ω| + f(q) near a Lifshitz point. The constant value for α = 4/5 and