Many-Body Description of van der Waals Torque in Two-Dimensional Materials

van der Waals (vdW) torque arising from quantum fluctuation of charge densities prevails in assemblies with anisotropic components and plays a key role in dictating the component alignments and physical properties of the system. Continuum Casimir-Lifshitz theory has been commonly employed to evaluate the vdW torque yet leaving the atomistic effects crucial in nanoscale systems essentially overlooked. By advancing a many-body dispersion model and using anisotropic two-dimensional materials as a prototype, we realize an ab initio description of the fundamental torque scaling laws previously established by continuum theory, such as the angular dependence of torque as -sin(2θ) with θ being interlayer disorientation angle and the positive correlation between torque and dielectric anisotropy ratio. Especially, we find nontrivial nanoscale effects on the torque, manifested as substantially modified torque magnitude and even torque-angle relation by tailoring shape, bending material, and adjusting relative orientation. Furthermore, our model demonstrates that the atomic force contributing vdW torque exhibits a nonlocal distribution rather than the intuitive local effect. These findings offer microscopic insights into the vdW torque and are instrumental for innovative explorations of anisotropic low-dimensional systems.