Universal Scaling of the Quantum Conductance of an Inversion-Symmetric Interacting Model

We consider quantum transport of spinless fermions in a 1D lattice embedding an interacting region (two sites with inter-site repulsion U and inter-site hopping td, coupled to leads by hopping terms tc). Using the numerical renormalization group for the particle-hole symmetric case, we study the quantum conductance g as a function of the inter-site hopping td. The interacting region, which is perfectly reflecting when td -> 0 or td -> infinity, becomes perfectly transmitting if td takes an intermediate value \tau(U,tc) which defines the characteristic energy of this interacting model. When td < tc sqrt(U), g is given by a universal function of the dimensionless ratio X=td/\tau. This universality characterizes the non-interacting regime where \tau=tc^2, the perturbative regime (U < tc^2) where \tau can be obtained using Hartree-Fock theory, and the non-perturbative regime (U > tc^2) where \tau is twice the characteristic temperature TK of an orbital Kondo effect induced by the inversion symmetry. When td < \tau, the expression g(X)=4/(X+1/X)^2 valid without interaction describes also the conductance in the presence of the interaction. To obtain those results, we map this spinless model onto an Anderson model with spins, where the quantum impurity is at the end point of a semi-infinite 1D lead and where td plays the role of a magnetic field h. This allows us to describe g(td) using exact results obtained for the magnetization m(h) of the Anderson model at zero temperature. We expect this universal scaling to be valid also in models with 2D leads, and observable using 2D semi-conductor heterostructures and an interacting region made of two identical quantum dots with strong capacitive inter-dot coupling and connected via a tunable quantum point contact.Comment: 14 pages, 18 figure

Effect of measurement probes upon the conductance of an interacting nanosystem: Detection of an attached ring by non local many body effects

We consider a nanosystem connected to measurement probes via leads. When a magnetic flux is varied through a ring attached to one lead at a distance Lc from the nanosystem, the effective nanosystem transmission |ts|^2 exhibits Aharonov-Bohm oscillations if the electrons interact inside the nanosystem. These oscillations can be very large if Lc is small and if the nanosystem has almost degenerate levels which are put near the Fermi energy by a local gate

Positive current cross-correlations in a highly transparent normal-superconducting beam splitter due to synchronized Andreev and inverse Andreev reflections

Predictions are established for linear differential current-current cross-correlations dSab/dV in a symmetrically biased three-terminal normal metal-superconductor-normal metal (NSN) device. Highly transparent contacts turn out to be especially interesting because they feature positive dSab/dV. At high transparency, processes based on Crossed Andreev Reflection (CAR) contribute only negligibly to the current and to dSab/dV. Under these circumstances, current-current cross-correlations can be plausibly interpreted as a coherent coupling between the two NS interfaces in the form of synchronized Andreev and inverse Andreev reflections, corresponding to the process where a pair of electron-like quasi-particles and a pair of hole-like quasi-particles arrive from the normal electrodes and annihilate in the superconductor. Hence, positive dSab/dV does not automatically imply CAR. For tunnel contacts, dSab/dV is positive because of CAR. In between these two extremities, at intermediate transparencies, dSab/dV is negative because both processes which cause positive correlations, occur only with small amplitude. We use scattering theory to obtain analytic expressions for current and noise, and microscopic calculation using a tight binding model in order to obtain a clear interpretation of the physical processes.Comment: 15 pages, 11 figures; Revised manuscript, analytical BTK-calculation, results not change

Optimal broadening of finite energy spectra in the numerical renormalization group: application to dissipative dynamics in two-level systems

Numerical renormalization group (NRG) calculations of quantum impurity models, based on a logarithmic discretization in energy of electronic or bosonic Hamiltonians, provide a powerful tool to describe physics involving widely separated energy scales, as typically encountered in nanostructures and strongly correlated materials. This main advantage of the NRG was however considered a drawback for resolving sharp spectral features at finite energy, such as dissipative atomic peaks. Surprisingly, we find a bunching of many-body levels in NRG spectra near dissipative resonances, and exploit this by combining the widely-used Oliveira's $z$-trick, using an averaging over {\it few} discrete NRG spectra, with an optimized {\it frequency-dependent} broadening parameter b(\w). This strategy offers a tremendous gain in computational power and extracts all the needed information from the raw NRG data without {\it a priori} knowledge of the various energy scales at play. As an application we investigate with high precision the crossover from coherent to incoherent dynamics in the spin boson model.Comment: 4 pages, 5 figures. Minor modifications in V

Attributing Low-level Storage Costs to High-Level Storage Operations in RPC Call Trees

Machines within a distributed computing network have a low-level storage system that provides remote procedure call (RPC) access to read/write files to their local disk/flash memory storage. Distributed computing networks support a library that facilitates the extraction of data flows between clients and storage systems. Attributing low-level storage operations to higher-level semantic operations is difficult because, seen from low-level storage, RPC calls are agnostic of high-level storage. This disclosure describes techniques to accurately attribute low-level storage costs to high-level storage operations in RPC call trees by maximizing a Jaccard similarity coefficient between two lists, e.g., a list of ancestor spans of each span in a trace associated with the low-level storage system, and a list of ancestor spans of each span in a trace associated with the library that facilitates the extraction of data flow between clients and storage systems. The described techniques find application in data governance and can be used to accurately estimate the resource usage associated with storage operations without making changes to logging or tracing logic

NRG Study of an Inversion-Symmetric Interacting Model: Universal Aspects of its Quantum Conductance

We consider scattering of spinless fermions by an inversion-symmetric interacting model characterized by three parameters (interaction U, internal hopping t_d and coupling t_c). Mapping this spinless model onto an Anderson model with Zeeman field, we use thenumerical renormalization group for studying the particle-hole symmetric case. We show that the zero temperature limit is characterized by a line of free-fermion fixed points and a scale \tau(U,t_c) of t_d for which there is perfect transmission. The quantum conductance and the low energy excitations of the model are given by universal functions of t_d/\tau if t_d \Gamma, \Gamma = t_c^2 being the level width of the scatterer. This universal regime becomes non-perturbative when U exceeds \Gamma.Comment: 4 pages 3 figure

Detection of interaction-induced nonlocal effects using perfectly transmitting nanostructures

We consider one-dimensional transport through an interacting region in series with a point-like one-body scatterer. When the conductance of the interacting region is perfect, independently of the interaction strength, a nonlocal interaction effect yields a total conductance of the composed system that depends on the interaction strength and is lower than the transmission of the one-body scatterer. This qualitative nonlocal effect allows to probe the dressing cloud of an interacting system by ideal noninteracting leads. The conductance correction increases with the strength of the interaction and the reflection of the one-body scatterer (attaining relative changes >50%), and decreases with the distance between the interacting region and the one-body scatterer. Scaling laws are obtained and possible experimental realizations are suggested.Comment: 6 pages, 6 figure

Dissipative spin dynamics near a quantum critical point: Numerical Renormalization Group and Majorana diagrammatics

We provide an extensive study of the sub-ohmic spin-boson model with power law density of states J(\omega)=\omega^s (with 0<s<1), focusing on the equilibrium dynamics of the three possible spin components, from very weak dissipation to the quantum critical regime. Two complementary methods, the bosonic Numerical Renormalization Group (NRG) and Majorana diagrammatics, are used to explore the physical properties in a wide range of parameters. We show that the bosonic self-energy is the crucial ingredient for the description of critical fluctuations, but that many-body vertex corrections need to be incorporated as well in order to obtain quantitative agreement of the diagrammatics with the numerical simulations. Our results suggest that the out-of-equilibrium dynamics in dissipative models beyond the Bloch-Redfield regime should be reconsidered in the long-time limit. Regarding also the spin-boson Hamiltonian as a toy model of quantum criticality, some of the insights gained here may be relevant for field theories of electrons coupled to bosons in higher dimensions.Comment: 19 pages, 19 figures. Minor changes in V

Scanning Gate Microscopy of a Nanostructure where Electrons Interact

We show that scanning gate microscopy can be used for probing electron-electron interactions inside a nanostructure. We assume a simple model made of two non-interacting strips attached to an interacting nanosystem. In one of the strips, the electrostatic potential can be locally varied by a charged tip. This change induces corrections upon the nanosystem Hartree-Fock self-energies which enhance the fringes spaced by half the Fermi wavelength in the images giving the quantum conductance as a function of the tip position

Production of non-local quartets and phase-sensitive entanglement in a superconducting beam splitter

Three BCS superconductors S_a, S_b, and S and two short normal regions N_a and N_b in a three-terminal S_aN_aSN_bS_b set-up provide a source of non-local quartets spatially separated as two correlated pairs in S_a and S_b, if the distance between the interfaces N_aS and SN_b is comparable to the coherence length in S. Low-temperature dc-transport of non-local quartets from S to S_a and S_b can occur in equilibrium, and also if S_a and S_b are biased at opposite voltages. At higher temperatures, thermal excitations result in correlated current fluctuations which depend on the superconducting phases phi_a and phi_b in S_a and S_b. Phase-sensitive entanglement is obtained at zero temperature if N_a and N_b are replaced by discrete levels.Comment: 4 pages, 2 figures; technical details attached in ancillary file http://arxiv.org/src/1102.2355v4/anc/EPAPS_Freyn_2011.pdf; higher versions: minor corrections, cleanup and corrected reference