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Register a new userPeriodic Anderson model with correlated conduction electrons: variational and exact diagonalization study
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We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the f-orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons, U_d, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher dimensional models. We find that this interaction shifts and widens the energy range of the bare f-level, where heavy-fermion behavior can be observed. For large enough U_d this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while U_d enhances the quasi-particle mass when the filling is close to half filling.
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We investigate an extended version of the periodic Anderson model where an interaction is switched on between the doubly occupied d- and f-sites. We perform variational calculations using the Gutzwiller trial wave function. We calculate the f-level occupancy as a function of the f-level energy with different interaction strengths. It is shown that the region of valence transition is sharpened due to the new interaction.
We have obtained the exact ground state wave functions of the Anderson-Hubbard model for different electron fillings on a 4x4 lattice with periodic boundary conditions - for 1/2 filling such ground states have roughly 166 million states. When compared to the uncorrelated ground states (Hubbard interaction set to zero) we have found strong evidence of the very effective screening of the charge homogeneities due to the Hubbard interaction. We have successfully modelled these local charge densities using a non-interacting model with a static screening of the impurity potentials. In addition, we have compared such wave functions to self-consistent real-space unrestricted Hartree-Fock solutions and have found that these approximate ground state wave functions are remarkably successful at reproducing the local charge densities, and may indicate the role of dipolar backflow in producing a novel metallic state in two dimensions.
We report on small-cluster exact-diagonalization calculations which prove the formation of electron-hole pairs (excitons) as prerequisite for spontaneous interlayer phase coherence in bilayer systems described by the extended Falicov-Kimball model. Evaluating the anomalous Greens function and momentum distribution function of the pairs, and thereby analyzing the dependence of the exciton binding energy, condensation amplitude, and coherence length on the Coulomb interaction strength, we demonstrate a crossover between a BCS-like electron-hole pairing transition and a Bose-Einstein condensation of tightly bound preformed excitons. We furthermore show that a mass imbalance between electrons and holes tends to suppress the condensation of excitons.
Recently, dynamical mean field theory calculations have shown that kinks emerge in the real part of the self energy of strongly correlated metals close to the Fermi level. This gives rise to a similar behavior in the quasi-particle dispersion relation as well as in the electronic specific heat. Since f-electron systems are even more strongly correlated than the -hitherto studied- d-electron systems we apply the dynamical mean field approach with the numerical renormalization group method as impurity solver to study whether there are kinks in the periodic Anderson model.
We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Within the latter, we derive an analytical expression for the adiabatic SCE Hartree exchange-correlation kernel in one dimensional systems, and we compute it numerically for a variety of model densities. We analyse the non-local features of this kernel, particularly the ones that are relevant in tackling problems where kernels derived from local or semi-local functionals are known to fail.
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