Exact scaling functions of the multichannel Kondo model

We reinvestigate the large degeneracy solution of the multichannel Kondo problem, and show how in the universal regime the complicated integral equations simplifying the problem can be mapped onto a first order differential equation. This leads to an explicit expression for the full zero-temperature scaling functions at - and away from - the intermediate non Fermi Liquid fixed point, providing complete analytic information on the universal low - and intermediate - energy properties of the model. These results also apply to the widely-used Non Crossing Approximation of the Anderson model, taken in the Kondo regime. An extension of this formalism for studying finite temperature effects is also proposed and offers a simple approach to solve models of strongly correlated electrons with relevance to the physics of heavy fermion compounds.Comment: 4 pages, 2 figures. Submitted to PRB. Minor changes in v

Microscopic bosonization of band structures: X-ray processes beyond the Fermi edge

Bosonization provides a powerful analytical framework to deal with one-dimensional strongly interacting fermion systems, which makes it a cornerstone in quantum many-body theory. Yet, this success comes at the expense of using effective infrared parameters, and restricting the description to low energy states near the Fermi level. We propose a radical extension of the bosonization technique that overcomes both limitations, allowing computations with microscopic lattice Hamiltonians, from the Fermi level down to the bottom of the band. The formalism rests on the simple idea of representing the fermion kinetic term in the energy domain, after which it can be expressed in terms of free bosonic degrees of freedom. As a result, one- and two-body fermionic scattering processes generate anharmonic boson-boson interactions, even in the forward channel. We show that up to moderate interaction strengths, these nonlinearities can be treated analytically at all energy scales, using the x-ray emission problem as a showcase. In the strong interaction regime, we employ a systematic variational solution of the bosonic theory, and obtain results that agree quantitatively with an exact diagonalization of the original one-particle fermionic model. This provides a proof of the fully microscopic character of bosonization on all energy scales for an arbitrary band structure. Besides recovering the known x-ray edge singularity at the emission threshold, we find strong signatures of correlations even at emission frequencies beyond the band bottom.Comment: 26 + 4 pages. Published versio

High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes

We study theoretically the energy and spatially resolved local density of states (LDoS) in graphene at high perpendicular magnetic field. For this purpose, we extend from the Schr\"odinger to the Dirac case a semicoherent-state Green's-function formalism, devised to obtain in a quantitative way the lifting of the Landau-level degeneracy in the presence of smooth confinement and smooth disordered potentials. Our general technique, which rigorously describes quantum-mechanical motion in a magnetic field beyond the semi-classical guiding center picture of vanishing magnetic length (both for the ordinary two-dimensional electron gas and graphene), is connected to the deformation (Weyl) quantization theory in phase space developed in mathematical physics. For generic quadratic potentials of either scalar (i.e., electrostatic) or mass (i.e., associated with coupling to the substrate) types, we exactly solve the regime of large magnetic field (yet at finite magnetic length - formally, this amounts to considering an infinite Fermi velocity) where Landau-level mixing becomes negligible. Hence, we obtain a closed-form expression for the graphene Green's function in this regime, providing analytically the discrete energy spectra for both cases of scalar and mass parabolic confinement. Furthermore, the coherent-state representation is shown to display a hierarchy of local energy scales ordered by powers of the magnetic length and successive spatial derivatives of the local potential, which allows one to devise controlled approximation schemes at finite temperature for arbitrary and possibly disordered potential landscapes. As an application, we derive general analytical non-perturbative expressions for the LDoS, which may serve as a good starting point for interpreting experimental studies.Comment: 27 pages, 2 figures ; v2: typos corrected, corresponds to published versio

Josephson-Kondo screening cloud in circuit quantum electrodynamics

We show that the non-local polarization response in a multimode circuit-QED setup, devised from a Cooper pair box coupled to a long chain of Josephson junctions, provides an alternative route to access the elusive Kondo screening cloud. For moderate circuit impedance, we compute analytically the universal lineshape for the decay of the charge susceptibility along the circuit, that relates to spatial entanglement between the qubit and its electromagnetic environment. At large circuit impedance, we numerically find further spatial correlations that are specific to a true many-body state.Comment: 4 pages, 3 figures (extra Supplementary Information attached

Universal spatial correlations in the anisotropic Kondo screening cloud: analytical insights and numerically exact results from a coherent state expansion

We analyze the spatial correlations in the spin density of an electron gas in the vicinity of a Kondo impurity. Our analysis extends to the spin-anisotropic regime, which was not investigated in the literature. We use an original and numerically exact method, based on a systematic coherent-state expansion of the ground state of the underlying spin-boson Hamiltonian, which we apply to the computation of observables that are specific to the fermionic Kondo model. We also present an important technical improvement to the method, that obviates the need to discretize modes of the Fermi sea, and allows one to tackle the problem in the thermodynamic limit. One can thus obtain excellent spatial resolution over arbitrary length scales, for a relatively low computational cost, a feature that gives the method an advantage over popular techniques such as NRG and DMRG. We find that the anisotropic Kondo model shows rich universal scaling behavior in the spatial structure of the entanglement cloud. First, SU(2) spin-symmetry is dynamically restored in a finite domain in parameter space in vicinity of the isotropic line, as expected from poor man's scaling. We are also able to obtain in closed analytical form a set of different, yet universal, scaling curves for strong exchange asymmetry, which are parametrized by the longitudinal exchange coupling. Deep inside the cloud, i.e. for distances smaller than the Kondo length, the correlation between the electron spin density and the impurity spin oscillates between ferromagnetic and antiferromagnetic values at the scale of the Fermi wavelength, an effect that is drastically enhanced at strongly anisotropic couplings. Our results also provide further numerical checks and alternative analytical approximations for the recently computed Kondo overlaps [PRL 114, 080601 (2015)].Comment: 27 pages + 2 pages of Supplementary materials. The manuscript was largely extended in V2, and contains now a comparison to the Toulouse limit, and well as a detailed study of the restoration of SU(2) symmetry. The displayed html abstract has been shortened compared to the pdf versio

Quantum transport properties of two-dimensional electron gases under high magnetic fields

We study quantum transport properties of two-dimensional electron gases under high perpendicular magnetic fields. For this purpose, we reformulate the high-field expansion, usually done in the operatorial language of the guiding-center coordinates, in terms of vortex states within the framework of real-time Green functions. These vortex states arise naturally from the consideration that the Landau levels quantization can follow directly from the existence of a topological winding number. The microscopic computation of the current can then be performed within the Keldysh formalism in a systematic way at finite magnetic fields $B$ (i.e. beyond the semi-classical limit $B = \infty$). The formalism allows us to define a general vortex current density as long as the gradient expansion theory is applicable. As a result, the total current is expressed in terms of edge contributions only. We obtain the first and third lowest order contributions to the current due to Landau-levels mixing processes, and derive in a transparent way the quantization of the Hall conductance. Finally, we point out qualitatively the importance of inhomogeneities of the vortex density to capture the dissipative longitudinal transport.Comment: 21 pages, 5 figures ; main change: the discussion about the longitudinal transport (Part A of Section VI) is rewritten and enhance

Dynamical Mean-Field Theory of Resonating Valence Bond Antiferromagnets

We propose a theory of the spin dynamics of frustrated quantum antiferromagnets, which is based on an effective action for a plaquette embedded in a self-consistent bath. This approach, supplemented by a low-energy projection, is applied to the kagome antiferromagnet. We find that a spin-liquid regime extends to very low energy, in which local correlation functions have a slow decay in time, well described by a power law behaviour and $\omega/T$ scaling of the response function: $\chi''(\omega)\propto \omega^{-\alpha}F(\omega/T)$.Comment: 5 pages, 3 figures; contains some clarifications on the role of the triplet states and the triplet ga

Transmission coefficient through a saddle-point electrostatic potential for graphene in the quantum Hall regime

From the scattering of semicoherent-state wavepackets at high magnetic field, we derive analytically the transmission coefficient of electrons in graphene in the quantum Hall regime through a smooth constriction described by a quadratic saddle-point electrostatic potential. We find anomalous half-quantized conductance steps that are rounded by a backscattering amplitude related to the curvature of the potential. Furthermore, the conductance in graphene breaks particle-hole symmetry in cases where the saddle-point potential is itself asymmetric in space. These results have implications both for the interpretation of split-gate transport experiments, and for the derivation of quantum percolation models for graphene.Comment: 4 pages, 2 figures Minor modifications as publishe

Dynamics of a Qubit in a High-Impedance Transmission Line from a Bath Perspective

We investigate quantum dynamics of a generic model of light-matter interaction in the context of high impedance waveguides, focusing on the behavior of the emitted photonic states, in the framework of the spin-boson model Quantum quenches as well as scattering of an incident coherent pulse are studied using two complementary methods. First, we develop an approximate ansatz for the electromagnetic waves based on a single multimode coherent state wavefunction; formally, this approach combines ideas from adiabatic renormalization, the Born-Markov approximation, and input-output theory. Second, we present numerically exact results for scattering of a weak intensity pulse by using NRG calculations. NRG provides a benchmark for any linear response property throughout the ultra-strong coupling regime. We find that in a sudden quantum quench, the coherent state approach produces physical artifacts, such as improper relaxation to the steady state. These previously unnoticed problems are related to the simplified form of the ansatz that generates spurious correlations within the bath. In the scattering problem, NRG is used to find the transmission and reflection of a single photon, as well as the inelastic scattering of that single photon. Simple analytical formulas are established and tested against the NRG data that predict quantitatively the transport coefficients for up to moderate environmental impedance. These formulas resolve pending issues regarding the presence of inelastic losses in the spin-boson model near absorption resonances, and could be used for comparison to experiments in Josephson waveguide QED. Finally, the scattering results using the coherent state wavefunction approach are compared favorably to the NRG results for very weak incident intensity. We end our study by presenting results at higher power where the response of the system is nonlinear.Comment: 11 pages, 11 figures. Minor changes in V

Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime

We develop in detail a new formalism [as a sequel to the work of T. Champel and S. Florens, Phys. Rev. B 75, 245326 (2007)] that is well-suited for treating quantum problems involving slowly-varying potentials at high magnetic fields in two-dimensional electron gases. For an arbitrary smooth potential we show that electronic Green's function is fully determined by closed recursive expressions that take the form of a high magnetic field expansion in powers of the magnetic length l_B. For illustration we determine entirely Green's function at order l_B^3, which is then used to obtain quantum expressions for the local charge and current electronic densities at equilibrium. Such results are valid at high but finite magnetic fields and for arbitrary temperatures, as they take into account Landau level mixing processes and wave function broadening. We also check the accuracy of our general functionals against the exact solution of a one-dimensional parabolic confining potential, demonstrating the controlled character of the theory to get equilibrium properties. Finally, we show that transport in high magnetic fields can be described hydrodynamically by a local equilibrium regime and that dissipation mechanisms and quantum tunneling processes are intrinsically included at the microscopic level in our high magnetic field theory. We calculate microscopic expressions for the local conductivity tensor, which possesses both transverse and longitudinal components, providing a microscopic basis for the understanding of dissipative features in quantum Hall systems.Comment: small typos corrected; published versio