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Register a new userReversal of particle-hole scattering-rate asymmetry in Anderson impurity model
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We study the particle-hole asymmetry of the scattering rate in strongly correlated electron systems by examining the cubic $omega^3$ and $omega T^2$ terms in the imaginary part of the self-energy of the Anderson impurity model. We show that the sign is opposite in the weak-coupling and strong-coupling limits, explaining the differences found in theoretical approaches taking the respective limits as the starting points. The sign change in fact precisely delineates the cross-over between the weak and strong correlation regimes of the model. For weak interaction $U$ the sign reversal occurs for small values of the doping $delta=1-n$, while for interaction of order $U approx 2 Gamma$, $Gamma$ being the hybridization strength, the cross-over curve rapidly shifts to the large-doping range. This curve based on the impurity dynamics is genuinely different from other cross-over curves defined through impurity thermodynamic and static properties.
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We study Gutzwiller-correlated wave functions as variational ground states for the two-impurity Anderson model (TIAM) at particle-hole symmetry as a function of the impurity separation ${bf R}$. Our variational state is obtained by applying the Gutzwiller many-particle correlator to a single-particle product state. We determine the optimal single-particle product state fully variationally from an effective non-interacting TIAM that contains a direct electron transfer between the impurities as variational degree of freedom. For a large Hubbard interaction $U$ between the electrons on the impurities, the impurity spins experience a Heisenberg coupling proportional to $V^2/U$ where $V$ parameterizes the strength of the on-site hybridization. For small Hubbard interactions we observe weakly coupled impurities. In general, for a three-dimensional simple cubic lattice we find discontinuous quantum phase transitions that separate weakly interacting impurities for small interactions from singlet pairs for large interactions.
We study the non-interacting two-impurity Anderson model on a lattice using the Green function equation-of-motion method. A case of particular interest is the RKKY limit that is characterized by a small hybridization between impurities and host electrons and the absence of a direct coupling between the impurities. In contrast to the low-density case, at half band-filling and particle-hole symmetry, the RKKY interaction decays as the inverse square of the impurity distance along the axis of a simple cubic lattice. In the RKKY limit, for the spectral function we generically observe a small splitting of the single-impurity resonance into two peaks. For a vanishing density-density correlation function of the host electrons, we find only a broadened single peak in the local density of states.
In this paper we examine the effects of electron-hole asymmetry as a consequence of strong correlations on the electronic Raman scattering in the normal state of copper oxide high temperature superconductors. Using determinant quantum Monte Carlo simulations of the single-band Hubbard model, we construct the electronic Raman response from single particle Greens functions and explore the differences in the spectra for electron and hole doping away from half filling. The theoretical results are compared to new and existing Raman scattering experiments on hole-doped La$_{2-x}$Sr$_{x}$CuO$_{4}$ and electron-doped Nd$_{2-x}$Ce$_{x}$CuO$_{4}$. These findings suggest that the Hubbard model with fixed interaction strength qualitatively captures the doping and temperature dependence of the Raman spectra for both electron and hole doped systems, indicating that the Hubbard parameter U does not need to be doping dependent to capture the essence of this asymmetry.
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.
A central feature of the Periodic Anderson Model is the competition between antiferromagnetism, mediated by the Ruderman-Kittel-Kasuya-Yosida interaction at small conduction electron-local electron hybridization $V$, and singlet formation at large $V$. At zero temperature, and in dimension $d>1$, these two phases are separated by a quantum critical point $V_c$. We use Quantum Monte Carlo simulations to explore the effect of impurities which have a local hybridization $V_{*} < V_c$ in the AF regime which are embedded in a bulk singlet phase with $V > V_c$. We measure the suppression of singlet correlations and the antiferromagnetic correlations which form around the impurity, as well as the size of the resulting domain. Our calculations agree qualitatively with NMR measurements in CeCoIn$_{5-x}$Cd$_x$.
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