A Hierarchical Approach to Quantum Many-Body Systems in Non-Markovian Environments
arXiv:2405.05093
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 and the Hierarchical Equations of Motion (HEOM) 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.
Added an appendix section to the derivation of the bath-correlation function, added clarifying statements to purification, corrected typos in text and equations