### Abstract

The auxiliary master equation approach [1,2] allows for a direct and efï¬�cient calculation of steady state properties of

correlated impurities out of equilibrium, as is needed, e.g., for non-equilibrium dynamical mean ï¬�eld theory (DMFT). It

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 dynamics of this auxiliary system are controlled by a Lindblad master equation whose

parameters are used to optimize the mapping, which quickly becomes exact upon increasing the number of bath orbitals.

Steady state and Greenâ€™s functions of the auxiliary system are evaluated by (non-hermitian) Lanczos exact diagonalization

or by matrix-product states (MPS). Dissipation is taken into account already with a small number of bath orbitals. We

discuss steady-state transport properties and spectrum of the Anderson impurity model in the presence of a voltage bias.

The splitting of the Kondo peak as function of voltage is discussed. The approach can be regarded as the non-equilibrium

steady-state extension of the exact-diagonalization or MPS-based DMFT, and introduces appropriate absorbing boundary

conditions for a many-body system.

correlated impurities out of equilibrium, as is needed, e.g., for non-equilibrium dynamical mean ï¬�eld theory (DMFT). It

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 dynamics of this auxiliary system are controlled by a Lindblad master equation whose

parameters are used to optimize the mapping, which quickly becomes exact upon increasing the number of bath orbitals.

Steady state and Greenâ€™s functions of the auxiliary system are evaluated by (non-hermitian) Lanczos exact diagonalization

or by matrix-product states (MPS). Dissipation is taken into account already with a small number of bath orbitals. We

discuss steady-state transport properties and spectrum of the Anderson impurity model in the presence of a voltage bias.

The splitting of the Kondo peak as function of voltage is discussed. The approach can be regarded as the non-equilibrium

steady-state extension of the exact-diagonalization or MPS-based DMFT, and introduces appropriate absorbing boundary

conditions for a many-body system.

Original language | English |
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Number of pages | 1 |

Publication status | Published - 23 Feb 2015 |

Event | Advanced Numerical Algorithms for Strongly Correlated Quantum Systems - Duration: 23 Feb 2015 → 26 Feb 2015 |

### Conference

Conference | Advanced Numerical Algorithms for Strongly Correlated Quantum Systems |
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Period | 23/02/15 → 26/02/15 |

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### Fields of Expertise

- Advanced Materials Science

### Cite this

Arrigoni, E. (2015).

*Auxiliary master equation approach for correlated quantum impurities out of equilibrium*. Advanced Numerical Algorithms for Strongly Correlated Quantum Systems, .