Nonequilibrium SteadyState Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States
Here, the numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but it faces limitations for steadystate 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 timedependent 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 zerobias conductance peak for the singleimpurity Anderson model.
 Authors:

^{[1]};
^{[2]};
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^{[3]}
 LudwigMaximiliansUniv., Munchen (Germany)
 Adam Mickiewicz Univ., Poznan (Poland)
 LudwigMaximiliansUniv., Munchen (Germany); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Report Number(s):
 BNL2093542018JAAM
Journal ID: ISSN 00319007; PRLTAO
 Grant/Contract Number:
 SC0012704
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 121; Journal Issue: 13; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
 OSTI Identifier:
 1480976
Schwarz, F., Weymann, I., von Delft, J., and Weichselbaum, Andreas. Nonequilibrium SteadyState Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States. United States: N. p.,
Web. doi:10.1103/PhysRevLett.121.137702.
Schwarz, F., Weymann, I., von Delft, J., & Weichselbaum, Andreas. Nonequilibrium SteadyState Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States. United States. doi:10.1103/PhysRevLett.121.137702.
Schwarz, F., Weymann, I., von Delft, J., and Weichselbaum, Andreas. 2018.
"Nonequilibrium SteadyState Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States". United States.
doi:10.1103/PhysRevLett.121.137702.
@article{osti_1480976,
title = {Nonequilibrium SteadyState Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States},
author = {Schwarz, F. and Weymann, I. and von Delft, J. and Weichselbaum, Andreas},
abstractNote = {Here, the numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but it faces limitations for steadystate 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 timedependent 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 zerobias conductance peak for the singleimpurity Anderson model.},
doi = {10.1103/PhysRevLett.121.137702},
journal = {Physical Review Letters},
number = 13,
volume = 121,
place = {United States},
year = {2018},
month = {9}
}
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 GoldhaberGordon, D.; Shtrikman, Hadas; Mahalu, D.
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