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Title: Nonequilibrium Steady-State Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States

Journal Article · · Physical Review Letters
 [1];  [2];  [1]; ORCiD logo [3]
  1. Ludwig-Maximilians-Univ., Munchen (Germany)
  2. Adam Mickiewicz Univ., Poznan (Poland)
  3. Ludwig-Maximilians-Univ., Munchen (Germany); Brookhaven National Lab. (BNL), Upton, NY (United States)

Here, the numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but it faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome by describing the thermal leads using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group. This yields quantitatively reliable results for the current (with errors ≲3%) down to the exponentially small energy scales characteristic of impurity models. We present results of benchmark quality for the temperature and magnetic field dependence of the zero-bias conductance peak for the single-impurity Anderson model.

Research Organization:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0012704
OSTI ID:
1480976
Report Number(s):
BNL-209354-2018-JAAM; PRLTAO
Journal Information:
Physical Review Letters, Vol. 121, Issue 13; ISSN 0031-9007
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 46 works
Citation information provided by
Web of Science

References (79)

Out-of-equilibrium dynamics in a quantum impurity model: Numerics for particle transport and entanglement entropy journal November 2017
Keldysh effective action theory for universal physics in spin- 1 2 Kondo dots journal March 2013
Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays journal August 2015
Real-time simulations of nonequilibrium transport in the single-impurity Anderson model journal June 2009
Spectral functions in one-dimensional quantum systems at finite temperature using the density matrix renormalization group journal June 2009
Transport properties and Kondo correlations in nanostructures: Time-dependent DMRG method applied to quantum dots coupled to Wilson chains journal November 2008
The renormalization group: Critical phenomena and the Kondo problem journal October 1975
Stable-unstable transition for a Bose-Hubbard chain coupled to an environment journal May 2018
Time-Dependent DMRG Study on Quantum Dot under a Finite Bias Voltage journal August 2008
Twofold Advance in the Theoretical Understanding of Far-From-Equilibrium Properties of Interacting Nanostructures journal September 2008
Green’s Functions from Real-Time Bold-Line Monte Carlo Calculations: Spectral Properties of the Nonequilibrium Anderson Impurity Model journal April 2014
A Tunable Kondo Effect in Quantum Dots journal July 1998
Spin- 1 2 Kondo effect in an InAs nanowire quantum dot: Unitary limit, conductance scaling, and Zeeman splitting journal December 2011
Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling : Equilibrium properties journal January 2018
Real-Time Evolution Using the Density Matrix Renormalization Group journal August 2004
Nonequilibrium Functional Renormalization Group for Interacting Quantum Systems journal October 2007
Finite-Temperature Dynamical Density Matrix Renormalization Group and the Drude Weight of Spin- 1 / 2 Chains journal May 2012
Anomalous Kondo Effect in a Quantum Dot at Nonzero Bias journal July 1999
Sum-Rule Conserving Spectral Functions from the Numerical Renormalization Group journal August 2007
Numerical renormalization group method for quantum impurity systems journal April 2008
Liouville space description of thermofields and their generalisations journal February 1987
Tensor networks and the numerical renormalization group journal December 2012
Comparative study of theoretical methods for non-equilibrium quantum transport journal April 2010
Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model journal September 2015
The density-matrix renormalization group in the age of matrix product states journal January 2011
Non-abelian symmetries in tensor networks: A quantum symmetry space approach journal December 2012
Conductance of inhomogeneous systems: Real-time dynamics journal July 2010
Calculating Green functions from finite systems journal April 2010
Flow equation calculation of transient and steady-state currents in the Anderson impurity model journal September 2010
Kondo model in nonequilibrium: Interplay between voltage, temperature, and crossover from weak to strong coupling journal August 2014
Steady-State Currents through Nanodevices: A Scattering-States Numerical Renormalization-Group Approach to Open Quantum Systems journal August 2008
Efficient Simulation of One-Dimensional Quantum Many-Body Systems journal July 2004
The Kondo Effect in the Unitary Limit journal September 2000
Kondo effect in a single-electron transistor journal January 1998
Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems journal June 2015
Scaling and Decoherence in the Nonequilibrium Kondo Model journal July 2005
Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems journal March 2013
Kondo-assisted and resonant tunneling via a single charge trap: A realization of the Anderson model out of equilibrium journal May 1994
Discarded weight and entanglement spectra in the numerical renormalization group journal September 2011
Local susceptibility and Kondo scaling in the presence of finite bandwidth journal February 2014
Exact solution of the Anderson model. II. Thermodynamic properties at finite temperatures journal April 1983
Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling: Nonequilibrium transport journal January 2018
Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach journal January 2018
Exact solution of the Anderson model: I journal April 1983
Alternative discretization in the numerical renormalization-group method journal September 2005
Thermofield-based chain-mapping approach for open quantum systems journal November 2015
Higher-Order Fermi-Liquid Corrections for an Anderson Impurity Away from Half Filling journal March 2018
At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model journal August 2018
Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states journal April 2010
Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states journal October 2015
Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: Theory and application to the current-voltage characteristics of the Anderson model journal January 2010
Lindblad-driven discretized leads for nonequilibrium steady-state transport in quantum impurity models: Recovering the continuum limit journal October 2016
Adaptive logarithmic discretization for numerical renormalization group methods journal August 2009
Universal line shape of the Kondo zero-bias anomaly in a quantum dot journal May 2012
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems journal June 2016
Nonequilibrium Transport through a Kondo Dot in a Magnetic Field: Perturbation Theory and Poor Man’s Scaling journal February 2003
Voltage Quench Dynamics of a Kondo System journal January 2016
Anomalous Kondo Effect in a Quantum Dot at Nonzero Bias text January 1999
Time-dependent DMRG Study on Quantum Dot under a Finite Bias Voltage text January 2008
Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures text January 2008
Adaptive logarithmic discretization for numerical renormalization group methods text January 2009
Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model text January 2009
Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States text January 2009
Comparative study of theoretical methods for nonequilibrium quantum transport text January 2010
The density-matrix renormalization group in the age of matrix product states text January 2010
Nonequilibrium Kondo model: Crossover from weak to strong coupling text January 2012
Universal lineshape of the Kondo zero-bias anomaly in a quantum dot text January 2012
Local susceptibility and Kondo scaling in the presence of finite bandwidth text January 2013
Thermofield-based chain mapping approach for open quantum systems text January 2015
Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model text January 2015
Out-of-equilibrium dynamics in a quantum impurity model: numerics for particle transport and entanglement entropy text January 2017
Stable-unstable transition for a Bose-Hubbard chain coupled to an environment text January 2017
Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling III: non-equilibrium transport text January 2017
Non-Equilibrium Transport through a Kondo-Dot in a Magnetic Field: Perturbation Theory and Poor Man's Scaling text January 2002
Real time evolution using the density matrix renormalization group text January 2004
The numerical renormalization group method for quantum impurity systems text January 2007
Anomalous Kondo-effect in Quantum Dot at non-zero bias text January 1998
Efficient simulation of one-dimensional quantum many-body systems text January 2003
Keldysh effective action theory for universal physics in spin-1/2 Kondo dots text January 2013

Cited By (13)

Lead geometry and transport statistics in molecular junctions journal June 2019
Real-time density-matrix coupled-cluster approach for closed and open systems at finite temperature journal October 2019
Magnetic field dependence of the thermopower of Kondo-correlated quantum dots: Comparison with experiment journal October 2019
Magnetic field dependence of the thermopower of Kondo-correlated quantum dots journal October 2019
Dynamics of Kondo voltage splitting after a quantum quench journal November 2019
Exact equilibrium results in the interacting resonant level model journal February 2019
Long-lived circulating currents in strongly correlated nanorings journal September 2019
Reconstructing Nonequilibrium Regimes of Quantum Many-Body Systems from the Analytical Structure of Perturbative Expansions journal October 2019
Exact equilibrium results in the Interacting Resonant Level Model text January 2018
Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions text January 2019
Dynamics of Kondo voltage splitting after a quantum quench text January 2019
Magnetic field dependence of the thermopower of Kondo-correlated quantum dots: Comparison with experiment text January 2019
Long-lived circulating currents in strongly correlated nanorings text January 2019