### Abstract

Abstract: We present a method to compute electronic steady state properties of

strongly correlated quantum systems out of equilibrium within dynamical mean-

ï¬�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 Greenâ€™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).

strongly correlated quantum systems out of equilibrium within dynamical mean-

ï¬�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 Greenâ€™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 language | English |
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Number of pages | 1 |

Publication status | Published - 17 Aug 2015 |

Event | Progress in Nonequilibrium Green's Functions VI - Lund Duration: 17 Aug 2015 → 21 Aug 2015 |

### Conference

Conference | Progress in Nonequilibrium Green's Functions VI |
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City | Lund |

Period | 17/08/15 → 21/08/15 |

### Fields of Expertise

- Advanced Materials Science

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## 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, .