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Register a new userGeneralized Schrieffer-Wolff Transformation of 2 Kondo Impurity Problem
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We have carried out a generalized Schrieffer-Wolff transformation of an Anderson two-impurity Hamiltonian to study the low-energy spin interactions of the system. The second-order expansion yields the standard Kondo Hamiltonian for two impurities with additional scattering terms. At fouth-order, we get the well-known RKKY interaction. In addition, we also find an antiferromagnetic superexchange coupling and a correlated Kondo coupling between the two impurities.
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We consider the Kondo effect arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the $C_{3}$ rotation symmetry, and we only retain the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) $propto 1/ [ | omega | ln ^{2}( Lambda /| omega | ) ] $ near the Dirac point $omega rightarrow 0$ even though the bulk density of states vanishes linearly. We study the resulting 3-impurity multi-channel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-$1/2$ doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity.
We study nonequilibrium thermoelectric transport properties of a correlated impurity connected to two leads for temperatures below the Kondo scale. At finite bias, for which a current flows across the leads, we investigate the differential response of the current to a temperature gradient. In particular, we compare the influence of a bias voltage and of a finite temperature on this thermoelectric response. This is of interest from a fundamental point of view to better understand the two different decoherence mechanisms produced by a bias voltage and by temperature. Our results show that in this respect the thermoelectric response behaves differently from the electric conductance. In particular, while the latter displays a similar qualitative behavior as a function of voltage and temperature, both in theoretical and experimental investigations, qualitative differences occur in the case of the thermoelectric response. In order to understand this effect, we analyze the different contributions in connection to the behavior of the impurity spectral function versus temperature. Especially in the regime of strong interactions and large enough bias voltages we obtain a simple picture based on the asymmetric suppression or enhancement of the split Kondo peaks as a function of the temperature gradient. Besides the academic interest, these studies could additionally provide valuable information to assess the applicability of quantum dot devices as responsive nanoscale temperature sensors.
We investigate the many-body effects of a magnetic adatom in ferromagnetic graphene by using the numerical renormalization group method. The nontrivial band dispersion of ferromagnetic graphene gives rise to interesting Kondo physics different from that in conventional ferromagnetic materials. For a half-filled impurity in undoped graphene, the presence of ferromagnetism can bring forth Kondo correlations, yielding two kink structures in the local spectral function near the Fermi energy. When the spin splitting of local occupations is compensated by an external magnetic field, the two Kondo kinks merge into a full Kondo resonance characterizing the fully screened ground state. Strikingly, we find the resulting Kondo temperature monotonically increases with the spin polarization of Dirac electrons, which violates the common sense that ferromagnetic bands are usually detrimental to Kondo correlations. Doped ferromagnetic graphene can behave as half metals, where its density of states at the Fermi energy linearly vanishes for one spin direction but keeps finite for the opposite direction. In this regime, we demonstrate an abnormal Kondo resonance that occurs in the first spin direction, while completely absent in the other one.
We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling $J_K$, longitudinal anisotropy $D$, and transverse anisotropy $E$. In the isotropic case, two impurities on opposite(same) sublattices have a singlet(triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively four-fold degenerate ground state, i.e., two decoupled impurities. For large enough $J_K$ the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear non-perturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persists and the two effects coexist: the impurities are underscreened, and the dangling spin-$1/2$ degrees of freedom are responsible for the inter-impurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasi-classical correlations.
An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits, the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method. This method does not require any ad hoc assumption on the structure of the Hamiltonian such as its linear response to applied fields. We numerically benchmark the local basis reduction method against other Hamiltonian reduction methods in the literature and report specific examples of superconducting qubits, including the capacitively-shunted flux qubit, where the standard reduction approaches fail. By combining the local basis reduction method with the Schrieffer-Wolff transformation we further extend its applicability to systems of interacting qubits and use it to extract both non-stoquastic two-qubit Hamiltonians and three-local interaction terms in three-qubit Hamiltonians.
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