No abstract

We show that the RKKY interaction in the two-impurity Anderson model comprise two contributions: a ferromagnetic part stemming from the symmetrized hybridization functions and an anti-ferromagnetic part. We demonstrate that this anti-ferromagnetic contribution can also be generated by an effective local tunneling term between the two impurities. This tunneling can be analytically calculated for particle-hole symmetric impurities. Replacing the full hybridization functions by the symmetric part and this tunneling term leads to the identical low-temperature fixed point spectrum in the numerical renormalization group. Compensating this tunneling term is used to restore the Varma-Jones quantum critical point between a strong coupling phase and a local singlet phase even in the absence of particle-hole symmetry in the hybridization functions. We analytically investigate the spatial frequencies of the effective tunneling term based on the combination of the band dispersion and the shape of the Fermi surface. Numerical renormalization group calculations provide a comparison of the distance dependent tunneling term and the local spin-spin correlation function. Derivations between the spatial dependency of the full spin-spin correlation function and the textbook RKKY interaction are reported.

No abstract

We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurityinduced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model (SIKM) on a tight-binding chain with bandwidth W = 2D where a spin-1/2 impurity at the chain center interacts with coupling strength JK with the local spin of the bath electrons. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact extrapolations obtained from the Density-Matrix Renormalization Group (DMRG) method and from the Numerical Renormalization Group (NRG) method performed with respect the inverse system size and Wilson parameter, respectively. In contrast to the Lanczos and Yosida wave functions, the Gutzwiller variational approach becomes exact in the strong-coupling limit, JK ≫ W , and reproduces the ground-state properties from DMRG and NRG for large couplings, JK W , with a high accuracy. For weak coupling, the Gutzwiller wave function describes a symmetry-broken state with an oriented local moment, in contrast to the exact solution. We calculate the impurity spin polarization and its susceptibility in the presence of magnetic fields that are applied globally or only locally to the impurity spin. The Yosida wave function provides qualitatively correct results in the weak-coupling limit. In DMRG, chains with about 10 3 sites are large enough to describe the susceptibilities down to JK/D ≈ 0.5. For smaller Kondo couplings, only the NRG provides reliable results for a general host-electron density of states ρ0(ǫ). To compare with results from Bethe Ansatz that become exact in the wideband limit, we study the impurity-induced magnetization and zero-field susceptibility. For small Kondo couplings, the zero-field susceptibilities at zero temperature approach χ0(JK ≪ D)/(gµB) 2 ≈ exp[1/(ρ0(0)JK)]/(2CD πeρ0(0)JK), where ln(C) is the regularized first inverse moment of the density of states. Using NRG, we determine the universal sub-leading corrections up to second order in ρ0(0)JK.

We show that the two-impurity Anderson model exhibits an additional quantum critical point at infinitely many specific distances between both impurities for an inversion symmetric onedimensional dispersion. Unlike the quantum critical point previously established,it is robust against particle-hole or parity symmetry breaking. The quantum critical point separates a spin doublet from a spin singlet ground state and is, therefore, protected. A finite single-particle tunneling t or an applied uniform gate voltage will drive the system across the quantum critical point. The discriminative magnetic properties of the different phases cause a jump in the spectral functions at low temperature, which might be useful for future spintronics devices. A local parity conservation will prevent the spin-spin correlation function from decaying to its equilibrium value after spin manipulations.