Steady-state dynamical mean-field theory within an auxiliary master equation approach

Enrico Arrigoni, Antonius Dorda, Martin Nuss, Michael Knap

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

Abstract

Abstract: We present a method to compute electronic steady state properties of
strongly correlated quantum systems out of equilibrium within dynamical mean-
�eld theory (DMFT) [1]. The DMFT correlated impurity problem is mapped onto
an auxiliary open system consisting of a small number of bath orbitals coupled to
the interacting impurity and to Markovian reservoirs described by a generalized
Lindblad equation [2,3]. The parameters of the auxiliary open system are used
to optimize the mapping, which becomes exponentially exact upon increasing the
number of bath orbitals. The auxiliary system is then solved by exact diagonali-
sation of the corresponding many-body non-Hermitian Lindblad equation, which
allows to evaluate Green’s functions directly in steady state upon bypassing the ini-
tial transient dynamics [3]. The approach can be regarded as the non-equilibrium
extension of the exact-diagonalization based DMFT, and introduces appropriate
absorbing boundary conditions for a many-body system out of equilibrium.
[1] J.K. Freericks et al., Phys. Rev. Lett. 97, 266408 (2006) [2] E. Arrigoni et al.,Phys. Rev. Lett. 110, 086403 (2013) [3] A. Dorda et al., Phys. Rev. B 89, 165105
(2014).

Original languageEnglish
Number of pages1
Publication statusPublished - 17 Aug 2015
EventProgress in Nonequilibrium Green's Functions VI - Lund
Duration: 17 Aug 201521 Aug 2015

Conference

ConferenceProgress in Nonequilibrium Green's Functions VI
CityLund
Period17/08/1521/08/15

Fingerprint

baths
orbitals
impurities
Green's functions
boundary conditions
electronics

Fields of Expertise

  • Advanced Materials Science

Cite this

Arrigoni, E., Dorda, A., Nuss, M., & Knap, M. (2015). Steady-state dynamical mean-field theory within an auxiliary master equation approach. Progress in Nonequilibrium Green's Functions VI, Lund, .

Steady-state dynamical mean-field theory within an auxiliary master equation approach. / Arrigoni, Enrico; Dorda, Antonius; Nuss, Martin; Knap, Michael.

2015. Progress in Nonequilibrium Green's Functions VI, Lund, .

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

Arrigoni, E, Dorda, A, Nuss, M & Knap, M 2015, 'Steady-state dynamical mean-field theory within an auxiliary master equation approach' Progress in Nonequilibrium Green's Functions VI, Lund, 17/08/15 - 21/08/15, .
Arrigoni E, Dorda A, Nuss M, Knap M. Steady-state dynamical mean-field theory within an auxiliary master equation approach. 2015. Progress in Nonequilibrium Green's Functions VI, Lund, .
Arrigoni, Enrico ; Dorda, Antonius ; Nuss, Martin ; Knap, Michael. / Steady-state dynamical mean-field theory within an auxiliary master equation approach. Progress in Nonequilibrium Green's Functions VI, Lund, .1 p.
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N2 - Abstract: We present a method to compute electronic steady state properties ofstrongly correlated quantum systems out of equilibrium within dynamical mean-�eld theory (DMFT) [1]. The DMFT correlated impurity problem is mapped ontoan auxiliary open system consisting of a small number of bath orbitals coupled tothe interacting impurity and to Markovian reservoirs described by a generalizedLindblad equation [2,3]. The parameters of the auxiliary open system are usedto optimize the mapping, which becomes exponentially exact upon increasing thenumber of bath orbitals. The auxiliary system is then solved by exact diagonali-sation of the corresponding many-body non-Hermitian Lindblad equation, whichallows to evaluate Green’s functions directly in steady state upon bypassing the ini-tial transient dynamics [3]. The approach can be regarded as the non-equilibriumextension of the exact-diagonalization based DMFT, and introduces appropriateabsorbing boundary conditions for a many-body system out of equilibrium.[1] J.K. Freericks et al., Phys. Rev. Lett. 97, 266408 (2006) [2] E. Arrigoni et al.,Phys. Rev. Lett. 110, 086403 (2013) [3] A. Dorda et al., Phys. Rev. B 89, 165105(2014).

AB - Abstract: We present a method to compute electronic steady state properties ofstrongly correlated quantum systems out of equilibrium within dynamical mean-�eld theory (DMFT) [1]. The DMFT correlated impurity problem is mapped ontoan auxiliary open system consisting of a small number of bath orbitals coupled tothe interacting impurity and to Markovian reservoirs described by a generalizedLindblad equation [2,3]. The parameters of the auxiliary open system are usedto optimize the mapping, which becomes exponentially exact upon increasing thenumber of bath orbitals. The auxiliary system is then solved by exact diagonali-sation of the corresponding many-body non-Hermitian Lindblad equation, whichallows to evaluate Green’s functions directly in steady state upon bypassing the ini-tial transient dynamics [3]. The approach can be regarded as the non-equilibriumextension of the exact-diagonalization based DMFT, and introduces appropriateabsorbing boundary conditions for a many-body system out of equilibrium.[1] J.K. Freericks et al., Phys. Rev. Lett. 97, 266408 (2006) [2] E. Arrigoni et al.,Phys. Rev. Lett. 110, 086403 (2013) [3] A. Dorda et al., Phys. Rev. B 89, 165105(2014).

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