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arXiv:1309.0027 · Journal of Statistical Mechanics Theory and Experiment

Real-space structure of the impurity screening cloud in the resonant level model

Shreyoshi Ghosh, Pedro Ribeiro, Masudul Haque

Published Apr 17, 2014• 19 citations
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Abstract

We present a detailed investigation of the impurity screening cloud in the resonant level model. The screening is visible in the structure of impurity–bath correlators as a function of distance from the impurity. We characterize the screening cloud through scaling analyses of impurity–bath correlators and entanglement entropies. We devise and study several situations where the screening cloud is destroyed or modified: finite temperatures, energetic detuning of the impurity from the chemical potential, and the situation of an unconventional bath with diverging density of states.

DOI
10.1088/1742-5468/2014/04/p04011

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We present a detailed investigation of the impurity screening cloud in the resonant level model. The screening is visible in the structure of impurity–bath correlators as a function of distance from the impurity. We characterize the screening cloud through scaling analyses of impurity–bath correlators and entanglement entropies. We devise and study several situations where the screening cloud is destroyed or modified: finite temperatures, energetic detuning of the impurity from the chemical potential, and the situation of an unconventional bath with diverging density of states.
We present a detailed investigation of the impurity screening cloud in the Resonant Level Model. The screening is visible in the structure of impurity-bath correlators as a function of distance from the impurity. We characterize the screening cloud through scaling analyses of impurity-bath correlators and entanglement entropies. We devise and study several situations where the screening cloud is destroyed or modified: finite temperatures, energetic detuning of the impurity from the chemical potential, and the situation of an unconventional bath with diverging density of states. ar X iv
We present a detailed analysis of the evolution of the impurity screening cloud in the resonant level model (RLM) followed by quenches of system parameters. The considered quenches are either local or found to be effectively local. The screening cloud is characterized by impurity-bath correlators and by the entanglement of a block centered around the impurity with the rest of the system. We consider several local quench protocols, such as, quenches from initially decoupled to coupled impurity, quenches between different finite couplings of the impurity, and 'detuning quenches' involving changing the onsite impurity potential away from or to the chemical potential of the bath. The relevant correlators and the entanglement display versions of the 'light-cone' effect, since the information about the quench travels through the bath at finite speed. At long times ('inside' the light cone), the impurity screening cloud relaxes exponentially to the final equilibrium structure, with the relaxation rate given by the emergent energy scale of impurity screening. Also, snapshots of the time-evolving spatial profile of impurity-bath correlators show exponential dependences on space, with the length scale given by the screening length.
We present a detailed analysis of the evolution of impurity screening cloud in the Resonant Level Model (RLM) followed by quenches of system parameters.The considered quenches are either local or found to be effectively local.The screening cloud is characterized by impurity-bath correlators and by the entanglement of a block centered around the impurity with the rest of the system.We consider several local quench protocols, such as, quenches from initially decoupled to coupled impurity, quenches between different finite couplings of the impurity, and 'detuning quenches' involving changing the onsite impurity potential away from or to the chemical potential of the bath.The relevant correlators and the entanglement display versions of the 'light-cone' effect, since the information about the quench travels through the bath at finite speed.At long times ('inside' the light cone), the impurity screening cloud relaxes exponentially to the final equilibrium structure, with the relaxation rate given by the emergent energy scale of impurity screening.Also, snaphots of the time-evolving spatial profile of impurity-bath correlators show exponential dependences on space, with the length scale given by the screening length.
Dynamical quantum impurities in metals induce electronic correlations in real space that are difficult to simulate due to their multiscale nature, so that only $s\text{\ensuremath{-}}\mathrm{wave}$ scattering in clean metallic hosts has been investigated so far. However, screening clouds should show anisotropy due to lack of full rotational invariance in two- and three-dimensional lattices, while inherent disorder will also induce spatial inhomogeneities. To tackle these challenges, we present an efficient and robust algorithm based on the recursive generation of natural orbitals defined as eigenvectors of the truncated single-particle density matrix. This method provides well-converged many-body wave functions on lattices with up to tens of thousands of sites, bypassing some limitations of other approaches. The algorithm is put to the test by investigating the charge screening cloud around an interacting resonant level, both on clean and disordered lattices, achieving accurate spatial resolution from short to long distances. We thus demonstrate strong anisotropy of spatial correlations around an adatom in the half-filled square lattice. Taking advantage of the efficiency of the algorithm, we further compute the disorder-induced distribution of Kondo temperatures over several thousands of random realizations, at the same time gaining access to the full spatial profile of the screening cloud in each sample. While the charge screening cloud is typically shortened due to the polarization of the impurity by the disorder potential, we surprisingly find that rare disorder configurations preserve the long-range nature of Kondo correlations in the electronic bath.
Abstract The screening of an impurity spin in the Kondo model occurs over a characteristic length scale ξ K , that defines the size of the Kondo screening cloud or ‘mist’. The presence of such a length scale in experimental and numerical results is rather subtle. A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations in terms of the single variable, r / ξ K instead of the correlations depending on r and ξ K separately. Here we study the paradigmatic one channel Kondo model using a spin chain representation, with an impurity spin at one end of the chain coupled with a strength J K ′ . Using Fermi liquid theory combined with numerical results, we obtain new high precision estimates of the non-universal terms in the entanglement entropy which leads to a verification of the expected non-integer ground-state degeneracy, g. This then allows us to study the impurity contribution to the entanglement in detail. If the impurity coupling J K ′ is varied, a precise determination of ξ K can then be obtained. The length scale, ξ K , is then shown to characterize the scaling of both the uniform and alternating part of a measure of the magnetization of part of an odd length chain.
The entanglement entropy in Kondo impurity systems is studied analytically using conformal field theory. From the impurity contribution to the scaling corrections of the entanglement entropy we extract information about the screening cloud profile for general non-Fermi-liquid fixed points. By also considering the finite-temperature corrections to scaling of the von Neumann entropy we point out a direct connection between the long-distance screening cloud profile and thermodynamic observables such as the specific heat.