Auxiliary master equation approach for strongly correlated quantum impurities out of equilibrium and applications within Dynamical Mean Field Theory

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

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, which becomes exponentially exact upon increasing the number of bath orbitals [3]. Green's functions are evaluated by (non-hermitian) Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [4].
Applications to nonequilibrium Dynamical Mean Field Theory (DMFT) [5] and a generalisation to treat periodically driven quantum systems within Floquet theory will be discussed. We present novel results of the (periodic-)steady state properties of an electric field driven mott insolator connected to non-interacting leads as a simplified model of a so called Mott Solar Cell''. The latter beeing a candidate of a highly efficient solar cell because of carier proliferation due to impact ionisation processes[6-8].

1. E. Arrigoni et al., Phys. Rev. Lett. {\bf110}, 086403 (2013).\newline
2. A. Dorda et al., Phys. Rev. B {\bf89} 165105 (2014).\newline
3. A. Dorda et al., arXiv {\bf1608}, 04632 (2016).\newline
4. A. Dorda et al., Phys. Rev. B {\bf92}, 125145 (2015).\newline
5. I. Titvinidze et al., Phys. Rev. B {\bf92}, 245125 (2015).\newline
6. E. Manousakis, Phys. Rev. B, {\bf82}, 125109, (2010).\newline
7. E. Assman et al., Phys. Rev. Lett. {\bf110}, 078701 (2013).\newline
8. M. Eckstein and P. Werner, Phys. Rev. Lett. {\bf113}, 076405 (2014).
Original language English Published - 24 Oct 2016 Workshop on Correlations, Integrability and Criticality in Quantum Systems - Univercity of Evora, Evora, PortugalDuration: 24 Oct 2016 → 28 Jan 2017http://www.cicqs.uevora.pt/

Conference

Conference Workshop on Correlations, Integrability and Criticality in Quantum Systems Portugal Evora 24/10/16 → 28/01/17 http://www.cicqs.uevora.pt/

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orbitals
impurities
baths
solar cells
time dependence
Green's functions
ionization
electric fields
products

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2016. Workshop on Correlations, Integrability and Criticality in Quantum Systems, Evora, Portugal.

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

Sorantin, ME, Dorda, A, von der Linden, W & Arrigoni, E 2016, 'Auxiliary master equation approach for strongly correlated quantum impurities out of equilibrium and applications within Dynamical Mean Field Theory' Workshop on Correlations, Integrability and Criticality in Quantum Systems, Evora, Portugal, 24/10/16 - 28/01/17, .
@conference{6f174198b0124265af88466a5c9bc603,
title = "Auxiliary master equation approach for strongly correlated quantum impurities out of equilibrium and applications within Dynamical Mean Field Theory",
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, which becomes exponentially exact upon increasing the number of bath orbitals [3]. Green's functions are evaluated by (non-hermitian) Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [4].Applications to nonequilibrium Dynamical Mean Field Theory (DMFT) [5] and a generalisation to treat periodically driven quantum systems within Floquet theory will be discussed. We present novel results of the (periodic-)steady state properties of an electric field driven mott insolator connected to non-interacting leads as a simplified model of a so called Mott Solar Cell''. The latter beeing a candidate of a highly efficient solar cell because of carier proliferation due to impact ionisation processes[6-8].1. E. Arrigoni et al., Phys. Rev. Lett. {\bf110}, 086403 (2013).\newline2. A. Dorda et al., Phys. Rev. B {\bf89} 165105 (2014).\newline3. A. Dorda et al., arXiv {\bf1608}, 04632 (2016).\newline4. A. Dorda et al., Phys. Rev. B {\bf92}, 125145 (2015).\newline5. I. Titvinidze et al., Phys. Rev. B {\bf92}, 245125 (2015).\newline6. E. Manousakis, Phys. Rev. B, {\bf82}, 125109, (2010).\newline7. E. Assman et al., Phys. Rev. Lett. {\bf110}, 078701 (2013).\newline8. M. Eckstein and P. Werner, Phys. Rev. Lett. {\bf113}, 076405 (2014).",
author = "Sorantin, {Max Erich} and Antonius Dorda and {von der Linden}, Wolfgang and Enrico Arrigoni",
year = "2016",
month = "10",
day = "24",
language = "English",
note = "Workshop on Correlations, Integrability and Criticality in Quantum Systems ; Conference date: 24-10-2016 Through 28-01-2017",
url = "http://www.cicqs.uevora.pt/",

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T1 - Auxiliary master equation approach for strongly correlated quantum impurities out of equilibrium and applications within Dynamical Mean Field Theory

AU - Sorantin, Max Erich

AU - Dorda, Antonius

AU - von der Linden, Wolfgang

AU - Arrigoni, Enrico

PY - 2016/10/24

Y1 - 2016/10/24

N2 - 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, which becomes exponentially exact upon increasing the number of bath orbitals [3]. Green's functions are evaluated by (non-hermitian) Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [4].Applications to nonequilibrium Dynamical Mean Field Theory (DMFT) [5] and a generalisation to treat periodically driven quantum systems within Floquet theory will be discussed. We present novel results of the (periodic-)steady state properties of an electric field driven mott insolator connected to non-interacting leads as a simplified model of a so called Mott Solar Cell''. The latter beeing a candidate of a highly efficient solar cell because of carier proliferation due to impact ionisation processes[6-8].1. E. Arrigoni et al., Phys. Rev. Lett. {\bf110}, 086403 (2013).\newline2. A. Dorda et al., Phys. Rev. B {\bf89} 165105 (2014).\newline3. A. Dorda et al., arXiv {\bf1608}, 04632 (2016).\newline4. A. Dorda et al., Phys. Rev. B {\bf92}, 125145 (2015).\newline5. I. Titvinidze et al., Phys. Rev. B {\bf92}, 245125 (2015).\newline6. E. Manousakis, Phys. Rev. B, {\bf82}, 125109, (2010).\newline7. E. Assman et al., Phys. Rev. Lett. {\bf110}, 078701 (2013).\newline8. M. Eckstein and P. Werner, Phys. Rev. Lett. {\bf113}, 076405 (2014).

AB - 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, which becomes exponentially exact upon increasing the number of bath orbitals [3]. Green's functions are evaluated by (non-hermitian) Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [4].Applications to nonequilibrium Dynamical Mean Field Theory (DMFT) [5] and a generalisation to treat periodically driven quantum systems within Floquet theory will be discussed. We present novel results of the (periodic-)steady state properties of an electric field driven mott insolator connected to non-interacting leads as a simplified model of a so called Mott Solar Cell''. The latter beeing a candidate of a highly efficient solar cell because of carier proliferation due to impact ionisation processes[6-8].1. E. Arrigoni et al., Phys. Rev. Lett. {\bf110}, 086403 (2013).\newline2. A. Dorda et al., Phys. Rev. B {\bf89} 165105 (2014).\newline3. A. Dorda et al., arXiv {\bf1608}, 04632 (2016).\newline4. A. Dorda et al., Phys. Rev. B {\bf92}, 125145 (2015).\newline5. I. Titvinidze et al., Phys. Rev. B {\bf92}, 245125 (2015).\newline6. E. Manousakis, Phys. Rev. B, {\bf82}, 125109, (2010).\newline7. E. Assman et al., Phys. Rev. Lett. {\bf110}, 078701 (2013).\newline8. M. Eckstein and P. Werner, Phys. Rev. Lett. {\bf113}, 076405 (2014).

M3 - (Old data) Lecture or Presentation

ER -