### 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.

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 language | English |
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Publication status | Published - 5 Sep 2016 |

Event | Quantum Dynamics: From Algorithms to Applications - Greifswald, Germany Duration: 5 Sep 2016 → 8 Sep 2016 http://theorie2.physik.uni-greifswald.de/qdyn16/ |

### Workshop

Workshop | Quantum Dynamics: From Algorithms to Applications |
---|---|

Country | Germany |

City | Greifswald |

Period | 5/09/16 → 8/09/16 |

Internet address |

### Cooperations

- NAWI Graz

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## 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.