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  • Open Access

Semigroup Influence Matrices for Nonequilibrium Quantum Impurity Models

Michael Sonner1,*, Valentin Link2,*, and Dmitry A. Abanin3,4

  • *These authors contributed equally to this work.
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Phys. Rev. Lett. 135, 170402 – Published 21 October, 2025

DOI: https://doi.org/10.1103/5gfn-l7w7

Abstract

We introduce a framework for describing the real-time dynamics of quantum impurity models out of equilibrium which is based on the influence matrix approach. By replacing the dynamical map of a large fermionic quantum environment with an effective semigroup influence matrix (SGIM) which acts on a reduced auxiliary space, we overcome the limitations of previous proposals, achieving high accuracy at long evolution times. This SGIM corresponds to a uniform matrix-product state representation of the influence matrix and can be obtained by an efficient algorithm presented in this Letter. We benchmark this approach by computing the spectral function of the single impurity Anderson model with high resolution. Further, the spectrum of the effective dynamical map allows us to obtain relaxation rates of the impurity toward equilibrium following a quantum quench. Finally, for a quantum impurity model with on-site two-fermion loss, we compute the spectral function and confirm the emergence of Kondo physics at large loss rates.

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Phys. Rev. Lett. 135, 170402– Published 21 October, 2025
  • Received 15 April 2025
  • Revised 17 July 2025
  • Accepted 22 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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