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Register a new userAnalytical and Numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity
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We study the conductance of a time-reversal symmetric helical electronic edge coupled antiferromagnetically to a magnetic impurity, employing analytical and numerical approaches. The impurity can reduce the perfect conductance $G_0$ of a noninteracting helical edge by generating a backscattered current. The backscattered steady-state current tends to vanish below the Kondo temperature $T_K$ for time-reversal symmetric setups. We show that the central role in maintaining the perfect conductance is played by a global $U(1)$ symmetry. This symmetry can be broken by an anisotropic exchange coupling of the helical modes to the local impurity. Such anisotropy, in general, dynamically vanishes during the renormalization group (RG) flow to the strong coupling limit at low-temperatures. The role of the anisotropic exchange coupling is further studied using the time-dependent Numerical Renormalization Group (TD-NRG) method, uniquely suitable for calculating out-of-equilibrium observables of strongly correlated setups. We investigate the role of finite bias voltage and temperature in cutting the RG flow before the isotropic strong-coupling fixed point is reached, extract the relevant energy scales and the manner in which the crossover from the weakly interacting regime to the strong-coupling backscattering-free screened regime is manifested. Most notably, we find that at low temperatures the conductance of the backscattering current follows a power-law behavior $Gsim (T/T_K)^2$, which we understand as a strong nonlinear effect due to time-reversal symmetry breaking by the finite-bias.
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Edge states of two-dimensional topological insulators are helical and single-particle backscattering is prohibited by time-reversal symmetry. In this work, we show that an isotropic exchange coupling of helical edge states (HES) to a spin 1/2 impurity subjected to a magnetic field results in characteristic backscattering current noise (BCN) as a function of bias voltage and tilt angle between the direction of the magnetic field and the quantization axis of the HES. In particular, we find transitions from sub-Poissonian (antibunching) to super-Poissonian (bunching) behavior as a direct consequence of the helicity of the edge state electrons. We use the method of full counting statistics within a master equation approach treating the exchange coupling between the spin-1/2 impurity and the HES perturbatively. We express the BCN via coincidence correlation functions of scattering processes between the HES which gives a precise interpretation of the Fano factor in terms of bunching and antibunching behavior of electron jump events. We also investigate the effect of electron-electron interactions in the HES in terms of the Tomonaga-Luttinger liquid theory.
We use different numerical approaches to calculate the double occupancy and mag- netic susceptibility as a function of a bias voltage in an Anderson impurity model. Specifically, we compare results from the Matsubara-voltage quantum Monte-Carlo approach (MV-QMC), the scattering-states numerical renormalization group (SNRG), and real-time quantum Monte-Carlo (RT-QMC), covering Coulomb repulsions ranging from the weak-coupling well into the strong- coupling regime. We observe a distinctly different behavior of the double occupancy and the magnetic response. The former measures charge fluctuations and thus only indirectly exhibits the Kondo scale, while the latter exhibits structures on the scale of the equilibrium Kondo tempera- ture. The Matsubara-voltage approach and the scattering-states numerical renormalization group yield consistent values for the magnetic susceptibility in the Kondo limit. On the other hand, all three numerical methods produce different results for the behavior of charge fluctuations in strongly interacting dots out of equilibrium.
We investigate the transport properties of Chern insulators following a quantum quench between topological and non-topological phases. Recent works have shown that this yields an excited state for which the Chern number is preserved under unitary evolution. However, this does not imply the preservation of other physical observables, as we stressed in our previous work. Here we provide an analysis of the Hall response following a quantum quench in an isolated system, with explicit results for the Haldane model. We show that the Hall conductance is no longer related to the Chern number in the post-quench state, in agreement with previous work. We also examine the dynamics of the edge currents in finite-size systems with open boundary conditions along one direction. We show that the late-time behavior is captured by a Generalized Gibbs Ensemble, after multiple traversals of the sample. We discuss the effects of generic open boundary conditions and confinement potentials.
We study equilibrium and nonequilibrium properties of the single-impurity Anderson model with a power-law pseudogap in the density of states. In equilibrium, the model is known to display a quantum phase transition from a generalized Kondo to a local moment phase. In the present work, we focus on the extension of these phases beyond equilibrium, i.e. under the influence of a bias voltage. Within the auxiliary master equation approach combined with a scheme based on matrix product states (MPS) we are able to directly address the current-carrying steady state. Starting with the equilibrium situation, we first corroborate our results by comparing with a direct numerical evaluation of ground state spectral properties of the system by MPS. Here, a scheme to locate the phase boundary by extrapolating the power-law exponent of the self energy produces a very good agreement with previous results obtained by the numerical renormalization group. Our nonequilibrium study as a function of the applied bias voltage is then carried out for two points on either side of the phase boundary. In the Kondo regime the resonance in the spectral function is splitted as a function of the increasing bias voltage. The local moment regime, instead, displays a dip in the spectrum near the position of the chemical potentials. Similar features are observed in the corresponding self energies. The Kondo split peaks approximately obey a power-law behavior as a function of frequency, whose exponents depend only slightly on voltage. Finally, the differential conductance in the Kondo regime shows a peculiar maximum at finite voltages, whose height, however, is below the accuracy level.
We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurity-induced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model on a tight-binding chain with bandwidth $W=2{cal D}$ and coupling strength $J_{rm K}$. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact data obtained from the Density-Matrix Renormalization Group (DMRG) and from the Numerical Renormalization Group (NRG) methods. The Gutzwiller variational approach becomes exact in the strong-coupling limit and reproduces the ground-state properties from DMRG and NRG for large couplings. We calculate the impurity spin polarization and its susceptibility in the presence of magnetic fields that are applied globally/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 $J_{rm K}/{cal D}approx 0.5$. For smaller Kondo couplings, only the NRG provides reliable results for a general host-electron density of states $rho_0(epsilon)$. To compare with results from Bethe Ansatz, we study the impurity-induced magnetization and zero-field susceptibility. For small Kondo couplings, the zero-field susceptibilities at zero temperature approach $chi_0(J_{rm K}ll {cal D})/(gmu_{rm B})^2approx exp[1/(rho_0(0)J_{rm K})]/(2C{cal D}sqrt{pi e rho_0(0)J_{rm K}})$, 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 $rho_0(0)J_{rm K}$.
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