21.15109/ARP/O4CEI6 Thiering, Gergő0000-0003-3357-5583(Wigner Research Centre for Physics)Gali, Ádám0000-0002-3339-5470(Wigner Research Centre for Physics) ARP 2025 hdl:21.15109/ARP/O4CEI6/4RA6SMhdl:21.15109/ARP/O4CEI6/FCXRUWhdl:21.15109/ARP/O4CEI6/YWKDJPhdl:21.15109/ARP/O4CEI6/DSSYTMhdl:21.15109/ARP/O4CEI6/T78QTRhdl:21.15109/ARP/O4CEI6/LQVSLIhdl:21.15109/ARP/O4CEI6/IUAXFDhdl:21.15109/ARP/O4CEI6/FDLSBThdl:21.15109/ARP/O4CEI6/3YWEDWhdl:21.15109/ARP/O4CEI6/8W0JFS Optically accessible solid state defect spins serve as a primary platform for quantum information processing, where precise control of the electron spin and ancillary nuclear spins is essential for operation. Using the nitrogen-vacancy (NV) color center in diamond as an example, we employ a combined group theory and density functional theory study to demonstrate that spin-lattice relaxation of the $^{14}$N nuclear spin is significantly enhanced due to strong entanglement with orbital degrees of freedom in the $|^3E\rangle$ optical excited state of the defect. This mechanism is common to other solid-state defect nuclear spins with similar optical excited states. Additionally, we propose a straightforward and versatile \textit{ab initio} scheme for predicting orbital-dependent spin Hamiltonians for trigonal defects exhibiting orbital degeneracy. Thiering, Gergő(Wigner Research Centre for Physics)