Auxiliary master equation approach for correlated quantum impurities out of equilibrium

Irakli Titvinidze, Antonius Dorda, Wolfgang von der Linden, Enrico Arrigoni

Research output: Contribution to conference(Old data) Lecture or PresentationResearch

Abstract

The auxiliary master equation approach [1,2] allows for an accurate and efficient treatment of
correlated impurities out of equilibrium. The method is based upon a mapping onto an auxiliary
open quantum system in which the impurity is coupled to bath orbitals as well as to a Markovian
environment. The intervening auxiliary orbitals allow for a treatment of non-Markovian
dynamics at the impurity. The time dependence of this auxiliary system is controlled by a
Lindblad master equation whose parameters are used to optimize the mapping. The auxiliary
system exponentially approaches the original impurity problem upon increasing the number
of parameters, i.e. of bath orbitals. Green’s functions are evaluated via (non-hermitian)
Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [3]. In particular, our
MPS implementation produces highly accurate spectral functions for nonequilibrium correlated
impurity problems in the Kondo regime. Specifically, we can treat large values of the interaction
and low temperatures T , well below the Kondo scale T K . For T = T K /4 and T = T K /10 we find
a splitting of the Kondo resonance into a two-peak structure at bias voltages just above T K . The
approach turns out to be an efficient impurity solver in equilibrium as well: a benchmark of our
results for T = T K /4 reveals a remarkably close agreement to numerical renormalization group.
Applications to nonequilibrium dynamical mean-field-theory [4] as well as an implementation
within Floquet theory for periodic driving [5] will be discussed as well.
References
[1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)
[2] A. Dorda et al., Phys. Rev. B 89 165105 (2014)
[3] A. Dorda et al., PRB 92, 125145 (2015)
[4] I. Titvinidze et al., PRB 92, 245125 (2015)
[5] M. Sorantin et al., in preparation.
Original languageEnglish
Publication statusPublished - 5 Sep 2016
EventQuantum Dynamics: From Algorithms to Applications - Greifswald, Germany
Duration: 5 Sep 20168 Sep 2016
http://theorie2.physik.uni-greifswald.de/qdyn16/

Workshop

WorkshopQuantum Dynamics: From Algorithms to Applications
CountryGermany
CityGreifswald
Period5/09/168/09/16
Internet address

Fingerprint

impurities
orbitals
baths
time dependence
Green's functions
preparation
electric potential
products

Cooperations

  • NAWI Graz

Cite this

Titvinidze, I., Dorda, A., von der Linden, W., & Arrigoni, E. (2016). Auxiliary master equation approach for correlated quantum impurities out of equilibrium. Quantum Dynamics: From Algorithms to Applications, Greifswald, Germany.

Auxiliary master equation approach for correlated quantum impurities out of equilibrium. / Titvinidze, Irakli; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico.

2016. Quantum Dynamics: From Algorithms to Applications, Greifswald, Germany.

Research output: Contribution to conference(Old data) Lecture or PresentationResearch

Titvinidze, I, Dorda, A, von der Linden, W & Arrigoni, E 2016, 'Auxiliary master equation approach for correlated quantum impurities out of equilibrium' Quantum Dynamics: From Algorithms to Applications, Greifswald, Germany, 5/09/16 - 8/09/16, .
Titvinidze I, Dorda A, von der Linden W, Arrigoni E. Auxiliary master equation approach for correlated quantum impurities out of equilibrium. 2016. Quantum Dynamics: From Algorithms to Applications, Greifswald, Germany.
Titvinidze, Irakli ; Dorda, Antonius ; von der Linden, Wolfgang ; Arrigoni, Enrico. / Auxiliary master equation approach for correlated quantum impurities out of equilibrium. Quantum Dynamics: From Algorithms to Applications, Greifswald, Germany.
@conference{e1da126e37df49e990f1f578ab1e0e64,
title = "Auxiliary master equation approach for correlated quantum impurities out of equilibrium",
abstract = "The auxiliary master equation approach [1,2] allows for an accurate and efficient treatment ofcorrelated impurities out of equilibrium. The method is based upon a mapping onto an auxiliaryopen quantum system in which the impurity is coupled to bath orbitals as well as to a Markovianenvironment. The intervening auxiliary orbitals allow for a treatment of non-Markoviandynamics at the impurity. The time dependence of this auxiliary system is controlled by aLindblad master equation whose parameters are used to optimize the mapping. The auxiliarysystem exponentially approaches the original impurity problem upon increasing the numberof parameters, i.e. of bath orbitals. Green’s functions are evaluated via (non-hermitian)Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [3]. In particular, ourMPS implementation produces highly accurate spectral functions for nonequilibrium correlatedimpurity problems in the Kondo regime. Specifically, we can treat large values of the interactionand low temperatures T , well below the Kondo scale T K . For T = T K /4 and T = T K /10 we finda splitting of the Kondo resonance into a two-peak structure at bias voltages just above T K . Theapproach turns out to be an efficient impurity solver in equilibrium as well: a benchmark of ourresults for T = T K /4 reveals a remarkably close agreement to numerical renormalization group.Applications to nonequilibrium dynamical mean-field-theory [4] as well as an implementationwithin Floquet theory for periodic driving [5] will be discussed as well.References[1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)[2] A. Dorda et al., Phys. Rev. B 89 165105 (2014)[3] A. Dorda et al., PRB 92, 125145 (2015)[4] I. Titvinidze et al., PRB 92, 245125 (2015)[5] M. Sorantin et al., in preparation.",
author = "Irakli Titvinidze and Antonius Dorda and {von der Linden}, Wolfgang and Enrico Arrigoni",
year = "2016",
month = "9",
day = "5",
language = "English",
note = "Quantum Dynamics: From Algorithms to Applications ; Conference date: 05-09-2016 Through 08-09-2016",
url = "http://theorie2.physik.uni-greifswald.de/qdyn16/",

}

TY - CONF

T1 - Auxiliary master equation approach for correlated quantum impurities out of equilibrium

AU - Titvinidze, Irakli

AU - Dorda, Antonius

AU - von der Linden, Wolfgang

AU - Arrigoni, Enrico

PY - 2016/9/5

Y1 - 2016/9/5

N2 - The auxiliary master equation approach [1,2] allows for an accurate and efficient treatment ofcorrelated impurities out of equilibrium. The method is based upon a mapping onto an auxiliaryopen quantum system in which the impurity is coupled to bath orbitals as well as to a Markovianenvironment. The intervening auxiliary orbitals allow for a treatment of non-Markoviandynamics at the impurity. The time dependence of this auxiliary system is controlled by aLindblad master equation whose parameters are used to optimize the mapping. The auxiliarysystem exponentially approaches the original impurity problem upon increasing the numberof parameters, i.e. of bath orbitals. Green’s functions are evaluated via (non-hermitian)Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [3]. In particular, ourMPS implementation produces highly accurate spectral functions for nonequilibrium correlatedimpurity problems in the Kondo regime. Specifically, we can treat large values of the interactionand low temperatures T , well below the Kondo scale T K . For T = T K /4 and T = T K /10 we finda splitting of the Kondo resonance into a two-peak structure at bias voltages just above T K . Theapproach turns out to be an efficient impurity solver in equilibrium as well: a benchmark of ourresults for T = T K /4 reveals a remarkably close agreement to numerical renormalization group.Applications to nonequilibrium dynamical mean-field-theory [4] as well as an implementationwithin Floquet theory for periodic driving [5] will be discussed as well.References[1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)[2] A. Dorda et al., Phys. Rev. B 89 165105 (2014)[3] A. Dorda et al., PRB 92, 125145 (2015)[4] I. Titvinidze et al., PRB 92, 245125 (2015)[5] M. Sorantin et al., in preparation.

AB - The auxiliary master equation approach [1,2] allows for an accurate and efficient treatment ofcorrelated impurities out of equilibrium. The method is based upon a mapping onto an auxiliaryopen quantum system in which the impurity is coupled to bath orbitals as well as to a Markovianenvironment. The intervening auxiliary orbitals allow for a treatment of non-Markoviandynamics at the impurity. The time dependence of this auxiliary system is controlled by aLindblad master equation whose parameters are used to optimize the mapping. The auxiliarysystem exponentially approaches the original impurity problem upon increasing the numberof parameters, i.e. of bath orbitals. Green’s functions are evaluated via (non-hermitian)Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [3]. In particular, ourMPS implementation produces highly accurate spectral functions for nonequilibrium correlatedimpurity problems in the Kondo regime. Specifically, we can treat large values of the interactionand low temperatures T , well below the Kondo scale T K . For T = T K /4 and T = T K /10 we finda splitting of the Kondo resonance into a two-peak structure at bias voltages just above T K . Theapproach turns out to be an efficient impurity solver in equilibrium as well: a benchmark of ourresults for T = T K /4 reveals a remarkably close agreement to numerical renormalization group.Applications to nonequilibrium dynamical mean-field-theory [4] as well as an implementationwithin Floquet theory for periodic driving [5] will be discussed as well.References[1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)[2] A. Dorda et al., Phys. Rev. B 89 165105 (2014)[3] A. Dorda et al., PRB 92, 125145 (2015)[4] I. Titvinidze et al., PRB 92, 245125 (2015)[5] M. Sorantin et al., in preparation.

M3 - (Old data) Lecture or Presentation

ER -