Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1503.06836 · Journal of Statistical Mechanics Theory and Experiment

Dynamics of the impurity screening cloud following quantum quenches of the resonant level model

Shreyoshi Ghosh, Pedro Ribeiro, Masudul Haque

Published Aug 6, 2015• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1742-5468/2015/08/p08002

Related papers

Dynamics of the impurity screening cloud following quantum quenches of the resonant level model

Ghosh, S., Ribeiro, P., Masudul Haque

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.

•Aug 6, 2015•7 citations

Real-space structure of the impurity screening cloud in the Resonant Level Model

Shreyoshi Ghosh, Pedro Ribeiro, Masudul Haque

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

•Apr 1, 2014•23 citations

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

Shreyoshi Ghosh, Pedro Ribeiro, Masudul Haque

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.

arXiv:1309.0027•Journal of Statistical Mechanics Theory and Experiment•Apr 17, 2014•19 citations

Nonequilibrium spatiotemporal formation of the Kondo screening cloud on a lattice

Martin Nuss, Martin Ganahl, Enrico Arrigoni +2 more

We study the nonequilibrium formation of a spin screening cloud that accompanies the quenching of a local magnetic moment immersed in a Fermi sea at zero temperature. Based on high-precision density matrix renormalization-group results for the interacting single-impurity Anderson model, we discuss the real-time evolution after a quantum quench in the impurity-reservoir hybridization using time-evolving block decimation. We report emergent length and time scales in the spatiotemporal structure of nonlocal correlation functions in the spin and the charge density channel. At equilibrium, our data for the correlation functions and the extracted length scales show good agreement with existing results, as do local time-dependent observables at the impurity. In the time-dependent data, we identify a major signal which defines a ``light cone'' moving at the Fermi velocity and a ferromagnetic component in its wake. Inside the light cone we find that the structure of the nonequilibrium correlation functions emerges on two time scales. Initially, the qualitative structure of the correlation functions develops rapidly at the lattice Fermi velocity. Subsequently the spin correlations converge to the equilibrium results on a much larger time scale. This process sets a dynamic energy scale, which we identify to be proportional to the Kondo temperature. Outside the light cone we observe two different power-law decays of the correlation functions in space, with time- and interaction-strength-independent exponents.

arXiv:1409.0646•Physical Review B•Feb 27, 2015•44 citations

Quench dynamics and relaxation of a spin coupled to interacting leads

Helena Bragança, Moallison F. Cavalcante, Rodrigo G. Pereira +1 more

We study a quantum quench in which a magnetic impurity is suddenly coupled to Hubbard chains, whose low-energy physics is described by Tomonaga-Luttinger liquid theory. Using the time-dependent density-matrix renormalization-group (tDMRG) technique, we analyze the propagation of charge, spin, and entanglement in the chains after the quench and relate the light-cone velocities to the dispersion of holons and spinons. We find that the local magnetization at the impurity site decays faster if we increase the interaction in the chains, even though the spin velocity decreases. We derive an analytical expression for the relaxation of the impurity magnetization which is in good agreement with the tDMRG results at intermediate timescales, providing valuable insight into the time evolution of the Kondo screening cloud in interacting systems.

arXiv:2101.09344•Physical review. B./Physical review. B•Mar 25, 2021•15 citations

Few-body nature of Kondo correlated ground states

Maxime Debertolis, Serge Florens, Izak Snyman

The quenching of degenerate impurity states in metals generally induces a long-range correlated quantum state known as the Kondo screening cloud. While a macroscopic number of particles clearly take part in forming this extended structure, assessing the number of truly entangled degrees of freedom requires a careful analysis of the relevant many-body wave function. For this purpose, we examine the natural single-particle orbitals that are eigenstates of the single-particle density (correlation) matrix for the ground state of two quantum impurity problems: the interacting resonant level model (IRLM) and the single impurity Anderson model (SIAM). As a simple and general probe for few-body versus many-body character we consider the rate of exponential decay of the correlation matrix eigenvalues towards inactive (fully empty or filled) orbitals. We find that this rate remains large in the physically most relevant region of parameter space, implying a few-body character. Genuine many-body correlations emerge only when the Kondo temperature becomes exponentially small, for instance near a quantum critical point. In addition, we demonstrate that a simple numerical diagonalization of the few-body problem restricted to the Fock space of the most correlated orbitals converges exponentially fast with respect to the number of orbitals, to the true ground state of the IRLM. We also show that finite-size effects drastically affect the correlation spectrum, shedding light on an apparent paradox arising from previous studies on short chains.

arXiv:2011.12678•Physical review. B./Physical review. B•Jun 29, 2021•23 citations
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.
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 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 study the nonequilibrium formation of a spin screening cloud that accompanies the quenching of a local magnetic moment immersed in a Fermi sea at zero temperature. Based on high-precision density matrix renormalization-group results for the interacting single-impurity Anderson model, we discuss the real-time evolution after a quantum quench in the impurity-reservoir hybridization using time-evolving block decimation. We report emergent length and time scales in the spatiotemporal structure of nonlocal correlation functions in the spin and the charge density channel. At equilibrium, our data for the correlation functions and the extracted length scales show good agreement with existing results, as do local time-dependent observables at the impurity. In the time-dependent data, we identify a major signal which defines a ``light cone'' moving at the Fermi velocity and a ferromagnetic component in its wake. Inside the light cone we find that the structure of the nonequilibrium correlation functions emerges on two time scales. Initially, the qualitative structure of the correlation functions develops rapidly at the lattice Fermi velocity. Subsequently the spin correlations converge to the equilibrium results on a much larger time scale. This process sets a dynamic energy scale, which we identify to be proportional to the Kondo temperature. Outside the light cone we observe two different power-law decays of the correlation functions in space, with time- and interaction-strength-independent exponents.
We study a quantum quench in which a magnetic impurity is suddenly coupled to Hubbard chains, whose low-energy physics is described by Tomonaga-Luttinger liquid theory. Using the time-dependent density-matrix renormalization-group (tDMRG) technique, we analyze the propagation of charge, spin, and entanglement in the chains after the quench and relate the light-cone velocities to the dispersion of holons and spinons. We find that the local magnetization at the impurity site decays faster if we increase the interaction in the chains, even though the spin velocity decreases. We derive an analytical expression for the relaxation of the impurity magnetization which is in good agreement with the tDMRG results at intermediate timescales, providing valuable insight into the time evolution of the Kondo screening cloud in interacting systems.
The quenching of degenerate impurity states in metals generally induces a long-range correlated quantum state known as the Kondo screening cloud. While a macroscopic number of particles clearly take part in forming this extended structure, assessing the number of truly entangled degrees of freedom requires a careful analysis of the relevant many-body wave function. For this purpose, we examine the natural single-particle orbitals that are eigenstates of the single-particle density (correlation) matrix for the ground state of two quantum impurity problems: the interacting resonant level model (IRLM) and the single impurity Anderson model (SIAM). As a simple and general probe for few-body versus many-body character we consider the rate of exponential decay of the correlation matrix eigenvalues towards inactive (fully empty or filled) orbitals. We find that this rate remains large in the physically most relevant region of parameter space, implying a few-body character. Genuine many-body correlations emerge only when the Kondo temperature becomes exponentially small, for instance near a quantum critical point. In addition, we demonstrate that a simple numerical diagonalization of the few-body problem restricted to the Fock space of the most correlated orbitals converges exponentially fast with respect to the number of orbitals, to the true ground state of the IRLM. We also show that finite-size effects drastically affect the correlation spectrum, shedding light on an apparent paradox arising from previous studies on short chains.