  The central topic of this letter is to show that light-matter hybridization
not only gives rise to novel dynamic responses but can also modify
intermolecular interactions and induce new structural order. Using the van der
Waals (vdW) system in an optical cavity as an example, we predict the effects
of interference and collectivity in cavity-induced many-body dispersion
interactions. Specifically, the leading order correction due to cavity-induced
quantum fluctuations leads to 3-body and 4-body vdW interactions, which can
align intermolecular vectors and are not pairwise additive. In addition, the
cavity-induced dipole leads to a single-molecule energy shift that aligns
individual molecules, and a pair-wise interaction that scales as $R^{-3}$
instead of the standard $R^{-6}$ distance scaling. The coefficients of all
these cavity-induced corrections depend on the cavity frequency and are
renormalized by the effective Rabi frequency, which in turn depends on the
particle density. Finally, we study the interaction of the vdW system in a
cavity with an external object and find a significant enhancement in the
interaction range due to modified distance scaling laws. These theoretical
predictions suggest the possibility of cavity-induced nematic or smectic order
and may provide an essential clue to understanding intriguing phenomena
observed in optical cavities, such as strongly-modified ground-state
reactivity, ion transport and solvent polarity.
