We show that the two impurity Anderson model exhibit an additional quantum critical point at infinitely many specific distances between both impurities for an inversion symmetric 1D dispersion. Unlike the quantum critical point previously established by Jones and Varma, 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, topological protected. A finite single particle tunneling
t or an applied uniform gate voltages 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 to decay to its equilibrium value after spin-manipulations.
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 one-dimensional 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.
We find the emergence of strong correlations and universality on the approach to the quantum critical points of a two-impurity Anderson model. The two impurities are coupled by an interimpurity exchange interaction J and direct interaction U{12} and are hybridized with separate conduction channels. The low energy behavior is described in terms of renormalized parameters. We show that on the approach to the transitions to a local singlet and a local charged ordered state, the quasiparticle weight factor z→0, and the renormalized parameters can be expressed in terms of a single energy scale T{*}. The values of the renormalized interaction parameters in terms of T{*} can be predicted from the condition of continuity of the spin and charge susceptibilities, and correspond to strong correlation. These predictions are confirmed by the numerical renormalization group calculations, including the case when the on site interaction U=0.
Since Jones-Varma seminal works the indirect RKKY interaction is usually modeled as independently tunable Heisenberg spin exchange. For such a model in particle-hole-symmetric case there is always a quantum phase transition between Kondo and RKKY phases, even in the resonant regime (i.e. when impurity-host coupling exceeds Coulomb interaction strength). We show, that for the simple model with RKKY interaction genuinely induced by Kondo couplings and the inter-host interaction, either two phase transitions occur or none, depending on the Kondo coupling strength. Each transition corresponds to destruction of effective quasi-particles by the relevant spin exchange and occurs at spin exchange strength of the order of the quasi-particle bandwidth. Similar results are expected for all quantum phase transitions induced by indirect interactions. Furthermore, we confirm earlier perturbative prediction of the Kondo breakdown at a finite Kondo temperature,
TK=TK0/e, with
TK meaning the scale where departure from high-energy local-moment regime happens, while strong-coupling or RKKY fixed points are achieved at arbitrarily small energy scales close to the transition. These findings may be relevant for heavy-fermion materials via DMFT mapping. We also propose experimental setup with 2-impurity system involving flat-band Moire material for direct test of our predictions.
We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct Coulomb interaction
U12 and a spin exchange interaction
J. The model has two types of quantum critical points, one at
J=Jc to a local singlet state and one at
U12=U12c to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale
T∗ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at
J=Jc. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.
We analyze the two-Anderson-impurity problem, in the strong-Coulomb-repulsion limit, by means of variational wave functions whose equations we solve analytically. We found two pairs of doublet states, one odd and one even with respect to the midplane between the impurities. These doublets make a significatively strong use of the hybridization terms of the Hamiltonian and have a much larger Kondo-like correlation energy than a single impurity (the Kondo energy). Furthermore, these doublets combine to form a supersinglet. This supersinglet makes use of the remaining hybridization probability to improve its energy with respect to the doublet energy, but for low-dimensional systems and at the interimpurity distances where the doublets are fully developed, its energy gain is exponentially small. The interaction behind the doublets is a first-order (in the effective Kondo coupling) one; it also generates a parallel alignment of the impurity spins. This ferromagnetic impurity-impurity response is thus generated without resort to the RKKY interaction. The effective range of this first-order Doublet interaction is also much larger than the one of the RKKY interaction.