We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is simply to replace densities of states by charge susceptibilities in formulas. In order to substantiate the Fermi liquid picture in the case of a quantum $RC$ geometry, we apply a renormalization group analysis and derive the low-energy Hamiltonian for two specific models: the Anderson and the Coulomb blockade models. The Anderson model is shown, using a field theoretical approach based on Barnes slave bosons, to map onto the Kondo model. We recover the well-known expression of the Kondo temperature for the asymmetric Anderson model and compute the charge susceptibility. The Barnes slave bosons are extended to the Coulomb blockade model where the renormalization-group analysis can be carried out perturbatively up to zero energy. All calculations agree with the Fermi liquid nature of the low-energy fixed point and satisfy the Friedel sum rule.We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is simply to replace densities of states by charge susceptibilities in formulas. In order to substantiate the Fermi liquid picture in the case of a quantum $RC$ geometry, we apply a renormalization group analysis and derive the low-energy Hamiltonian for two specific models: the Anderson and the Coulomb blockade models. The Anderson model is shown, using a field theoretical approach based on Barnes slave bosons, to map onto the Kondo model. We recover the well-known expression of the Kondo temperature for the asymmetric Anderson model and compute the charge susceptibility. The Barnes slave bosons are extended to the Coulomb blockade model where the renormalization-group analysis can be carried out perturbatively up to zero energy. All calculations agree with the Fermi liquid nature of the low-energy fixed point and satisfy the Friedel sum rule.

arXiv:1205.2213Physical Review BSep 12, 201227 citations

Electric dipolar susceptibility of the Anderson-Holstein model

Takahiro Fuse, Takashi Hotta

The temperature dependence of the electric dipolar susceptibility χP is discussed on the basis of the Anderson-Holstein model with the use of a numerical renormalization group (NRG) technique. Note that χ P is related to the phonon Green’s function D. In order to obtain a correct temperature dependence for χ P at low temperatures, we propose a method to evaluate χ P through the Dyson equation from the charge susceptibility χ c calculated by using the NRG instead of the direct NRG calculation of D. We find that the irreducible charge susceptibility estimated from χ c agree with the perturbation calculation, suggesting that our method works well.The temperature dependence of the electric dipolar susceptibility χP is discussed on the basis of the Anderson-Holstein model with the use of a numerical renormalization group (NRG) technique. Note that χ P is related to the phonon Green’s function D. In order to obtain a correct temperature dependence for χ P at low temperatures, we propose a method to evaluate χ P through the Dyson equation from the charge susceptibility χ c calculated by using the NRG instead of the direct NRG calculation of D. We find that the irreducible charge susceptibility estimated from χ c agree with the perturbation calculation, suggesting that our method works well.

arXiv:1207.2599Journal of the Korean Physical SocietyJun 1, 20134 citations

On the high temperature susceptibility of the Heisenberg model

David W. Wood

Physics LettersFeb 1, 19656 citations

RC

geometry, we apply a renormalization group analysis and derive the low-energy Hamiltonian for two specific models: the Anderson and the Coulomb blockade models. The Anderson model is shown, using a field theoretical approach based on Barnes slave bosons, to map onto the Kondo model. We recover the well-known expression of the Kondo temperature for the asymmetric Anderson model and compute the charge susceptibility. The Barnes slave bosons are extended to the Coulomb blockade model where the renormalization-group analysis can be carried out perturbatively up to zero energy. All calculations agree with the Fermi liquid nature of the low-energy fixed point and satisfy the Friedel sum rule.