Lindblad-driven discretized leads for nonequilibrium steady-state transport in quantum impurity models: Recovering the continuum limit

F. Schwarz, M. Goldstein, Antonius Dorda, Enrico Arrigoni, A. Weichselbaum, J. Von Delft

Research output: Contribution to journalArticleResearchpeer-review

Abstract

The description of interacting quantum impurity models in steady-state nonequilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing a truly open quantum system are seemingly incompatible. One possibility to bridge this gap is the use of Lindblad-driven discretized leads (LDDL): one couples auxiliary continuous reservoirs to the discretized lead levels and represents these additional reservoirs by Lindblad terms in the Liouville equation. For quadratic models governed by Lindbladian dynamics, we present an elementary approach for obtaining correlation functions analytically. In a second part, we use this approach to explicitly discuss the conditions under which the continuum limit of the LDDL approach recovers the correct representation of thermal reservoirs. As an analytically solvable example, the nonequilibrium resonant level model is studied in greater detail. Lastly, we present ideas towards a numerical evaluation of the suggested Lindblad equation for interacting impurities based on matrix product states. In particular, we present a reformulation of the Lindblad equation, which has the useful property that the leads can be mapped onto a chain where both the Hamiltonian dynamics and the Lindblad driving are local at the same time. Moreover, we discuss the possibility to combine the Lindblad approach with a logarithmic discretization needed for the exploration of exponentially small energy scales.

Original languageEnglish
Article number155142
JournalPhysical Review / B
Volume94
Issue number15
DOIs
Publication statusPublished - 27 Oct 2016

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Impurities
continuums
impurities
Lead
Liouville equation
Hamiltonians
requirements
Liouville equations
evaluation
products
energy
Hot Temperature

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Fields of Expertise

  • Advanced Materials Science

Cite this

Lindblad-driven discretized leads for nonequilibrium steady-state transport in quantum impurity models : Recovering the continuum limit. / Schwarz, F.; Goldstein, M.; Dorda, Antonius; Arrigoni, Enrico; Weichselbaum, A.; Von Delft, J.

In: Physical Review / B, Vol. 94, No. 15, 155142, 27.10.2016.

Research output: Contribution to journalArticleResearchpeer-review

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