Gutzwiller variational approach to the two-impurity Anderson model at particle-hole symmetry

Abstract

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 $\mathbf{R}$. 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.

arXiv comment24 pages, 10 figures, submitted to J. Phys. Cond. Matt

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Cited by in corpus (4)

• Effective low-energy description of the two impurity Anderson model: RKKY interaction and quantum criticality
• Symmetric single-impurity Kondo model on a tight-binding chain: a comparison of analytical and numerical ground-state approaches
• Ground-state properties of the symmetric single-impurity Anderson model on a ring from Density-Matrix Renormalization Group, Hartree-Fock, and Gutzwiller theory
• Non-interacting two-impurity Anderson model on a lattice at particle-hole symmetry