Second Quantization of Many-Body Dispersion Formalism: Towards Efficient Quantum Modeling of Million-Atom Systems in Complex Environments

Dispersive van der Waals and Casimir interactions play a key role in an accurate description of the structure, stability, and dynamical properties in physical, chemical, and biological systems. In particular, the many-body dispersion (MBD) formalism, relying on a system of electrostatically coupled quantum harmonic oscillators, provides a tool to understand and numerically investigate many-body van der Waals interactions in systems up to tens of thousands of atoms [Chemical Society Reviews 48, 4118 (2019)]. However, the analysis of MBD collective normal modes in such large systems is not trivial. Moreover, it is not easy to define the coupling among such plasmon-like modes with the degrees of freedom of the surrounding environment (phonons, photons, polaritons). We present a quantum field theoretical approach based on second quantization formalism to describe MBD modes. Such a theoretical description i) enables improved computational efficiency, ii) allows a straightforward application of quantum information tools to MBD modes analysis, and iii) provides a suitable framework to describe the interaction of MBD modes with the surrounding environment. This paves the way to describe MBD effects in large systems such as realistic biomolecular complexes in an arbitrary environment.