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Register a new userExtremely Correlated Fermi Liquid study of the U=infinity Anderson Impurity Model
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We apply the recently developed extremely correlated Fermi liquid theory to the Anderson impurity model, in the extreme correlation limit. We develop an expansion in a parameter lambda, related to n_d, the average occupation of the localized orbital, and find analytic expressions for the Greens functions to O(lambda^2). These yield the impurity spectral function and also the self-energy Sigma(omega) in terms of the two self energies of the ECFL formalism. The imaginary parts of the latter, have roughly symmetric low energy behaviour (~ omega^2), as predicted by Fermi Liquid theory. However, the inferred impurity self energy Sigma(omega) develops asymmetric corrections near n_d ~ 1, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation the Friedel sum rule is satisfied but we overestimate the quasiparticle weight z relative to the known exact results, resulting in an over broadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight z, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities.
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We study the two-dimensional $t$-$J$ model with second neighbor hopping parameter $t$ and in a broad range of doping $delta$ using a closed set of equations from the {em Extremely Correlated Fermi Liquid} (ECFL) theory. We obtain asymmetric energy distribution curves and symmetric momentum distribution curves of the spectral function, consistent with experimental data. We further explore the Fermi surface and local density of states for different parameter sets. Using the spectral function, we calculate the resistivity, Hall number and spin susceptibility. The curvature change in the resistivity curves with varying $delta$ is presented and connected to intensity loss in Angle Resolved Photoemission Spectroscopy (ARPES) experiments. We also discuss the role of the super-exchange $J$ in the spectral function and the resistivity in the optimal to overdoped density regimes.
Low energy properties of the metallic state of the 2-dimensional tJ model are presented at various densities and temperatures for second neighbor hopping t, with signs that are negative or positive corresponding to hole or electron doping. The calculation employs a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations, when used in $d=infty$ reproduce most of the known low energies features of the $U=infty$ Hubbard model. In 2-dimensions we are able to study the variations due to the superexchange J. The resulting Dyson self energy is found to be momentum dependent as expected. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity and cotangent of the Hall angle in experimentally relevant units. These display significant thermal sensitivity for density n >~ 0.8, signifying an effective Fermi-liquid temperature scale which is two or three orders of magnitude below the bare bandwidth. Flipping the sign of the hopping t, i.e. studying hole versus electron doping, is found to induce a change in curvature of the temperature dependent resistivity from convex to concave at low temperatures. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.
We present the detailed formalism of the extremely correlated Fermi liquid theory, developed for treating the physics of the t-J model. We start from the exact Schwinger equation of motion for the Greens function for projected electrons, and develop a systematic expansion in a parameter lambda, relating to the double occupancy. The resulting Greens function has a canonical part arising from an effective Hamiltonian of the auxiliary electrons, and a caparison part, playing the role of a frequency dependent adaptive spectral weight. This adaptive weight balances the requirement at low omega, of the invariance of the Fermi volume, and at high omega, of decaying as c_0/(i omega), with a correlation depleted c_0 <1. The effective Hamiltonian H_{eff} describing the auxiliary Fermions is given a natural interpretation with an effective interaction V_{eff} containing both the exchange J(ij), and the hopping parameters t(ij). It is made Hermitian by adding suitable terms that ultimately vanish, in the symmetrized theory developed in this paper. Simple but important shift invariances of the t-J model are noted with respect to translating its parameters uniformly. These play a crucial role in constraining the form of V_{eff} and also provide checks for further approximations. The auxiliary and physical Greens function satisfy two sum rules, and the Lagrange multipliers for these are identified. A complete set of expressions for the Greens functions to second order in lambda is given, satisfying various invariances. A systematic iterative procedure for higher order approximations is detailed. A superconducting instability of the theory is noted at the simplest level with a high transition temperature.
We investigate static and dynamical ground-state properties of the two-impurity Anderson model at half filling in the limit of vanishing impurity separation using the dynamical density-matrix renormalization group method. In the weak-coupling regime, we find a quantum phase transition as function of inter-impurity hopping driven by the charge degrees of freedom. For large values of the local Coulomb repulsion, the transition is driven instead by a competition between local and non-local magnetic correlations. We find evidence that, in contrast to the usual phenomenological picture, it seems to be the bare effective exchange interactions which trigger the observed transition.
We study the two-impurity Anderson model on finite chains using numerical techniques. We discuss the departure of magnetic correlations as a function of the interimpurity distance from a pure 2k_F oscillation due to open boundary conditions. We observe qualitatively different behaviors in the interimpurity spin correlations and in transport properties at different values of the impurity couplings. We relate these different behaviors to a change in the relative dominance between the Kondo effect and the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction. We also observe that when RKKY dominates there is a definite relation between interimpurity magnetic correlations and transport properties. In this case, there is a recovery of 2k_F periodicity when the on-site Coulomb repulsion on the chain is increased at quarter-filling. The present results could be relevant for electronic nanodevices implementing a non-local control between two quantum dots that could be located at variable distance along a wire.
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