### Abstract

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 |

### Fingerprint

### Fields of Expertise

- Advanced Materials Science

### Cite this

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

**Auxiliary master equation approach for correlated quantum impurities out of equilibrium.** / Arrigoni, Enrico.

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

}

TY - CONF

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

AU - Arrigoni, Enrico

PY - 2015/2/23

Y1 - 2015/2/23

N2 - The auxiliary master equation approach [1,2] allows for a direct and efï¬�cient calculation of steady state properties ofcorrelated impurities out of equilibrium, as is needed, e.g., for non-equilibrium dynamical mean ï¬�eld theory (DMFT). Itis based upon a mapping onto an auxiliary open quantum system in which the impurity is coupled to bath orbitals as wellas to a Markovian environment. The dynamics of this auxiliary system are controlled by a Lindblad master equation whoseparameters 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 diagonalizationor by matrix-product states (MPS). Dissipation is taken into account already with a small number of bath orbitals. Wediscuss 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-equilibriumsteady-state extension of the exact-diagonalization or MPS-based DMFT, and introduces appropriate absorbing boundaryconditions for a many-body system.

AB - The auxiliary master equation approach [1,2] allows for a direct and efï¬�cient calculation of steady state properties ofcorrelated impurities out of equilibrium, as is needed, e.g., for non-equilibrium dynamical mean ï¬�eld theory (DMFT). Itis based upon a mapping onto an auxiliary open quantum system in which the impurity is coupled to bath orbitals as wellas to a Markovian environment. The dynamics of this auxiliary system are controlled by a Lindblad master equation whoseparameters 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 diagonalizationor by matrix-product states (MPS). Dissipation is taken into account already with a small number of bath orbitals. Wediscuss 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-equilibriumsteady-state extension of the exact-diagonalization or MPS-based DMFT, and introduces appropriate absorbing boundaryconditions for a many-body system.

UR - https://for1807.physik.uni-wuerzburg.de/wp-content/uploads/2015/02/booklet6.pdf

M3 - (Old data) Lecture or Presentation

ER -