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Hierarchical approach to quantum many-body systems in non-Markovian environments

Kai Müller1, Kimmo Luoma2, and Christian Schäfer3,*

  • *Contact author: christian.schaefer@tuwien.ac.at
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Phys. Rev. B 114, 204301 – Published 8 October, 2026

DOI: https://doi.org/10.1103/6x28-j46x

Abstract

Quantum many-body systems in cavities combine the rich physics of condensed matter systems or quantum chemistry with strong coupling to the surrounding electromagnetic field. In these systems, large Hilbert spaces, many-body interactions, and strong system-environment coupling are all fundamental, posing a significant barrier for established methods in quantum optics and condensed matter physics. Here we propose a novel method based on a combination of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy [M. Bonitz, Quantum Kinetic Theory (Springer International Publishing, Cham, 2016)] and the Hierarchical Equations of Motion (HEOM) [Y. Tanimura, Phys. Rev. A 41, 6676 (1990)] to achieve a rigorous description of open many-body systems in contact with structured photonic and phononic baths. We rationalize that this stacked hierarchy accounts for spin squeezing and superradiant emission despite its applicability to arbitrarily many emitters. The potential of BBGKY-HEOM is then demonstrated for many-body electronic systems embedded in host materials (e.g., molecules in organic crystals). We show that the impact of phononic coupling and charge noise can be as relevant as electronic correlation. Our work establishes an accessible, yet rigorous, route between condensed matter and quantum optics, fostering the growth of a new domain at their interface.

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Phys. Rev. B 114, 204301– Published 8 October, 2026
  • Received 31 July 2025
  • Revised 24 August 2026
  • Accepted 14 September 2026
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