Spin Relaxation Mechanisms and Nuclear Spin Entanglement of the VB⁻¹ Center in hBN

The negatively charged boron vacancy VB⁻ defect in hexagonal boron nitride (hBN) has recently emerged as a promising spin qubit for sensing due to its high-temperature spin control and versatile integration into van der Waals structures. While extensive experiments have explored their coherence properties, much less is known about the spin relaxation time T₁ and its control-parameter dependence. In this work, we develop a parameter-free spin dynamics model based on the cluster-expansion technique to investigate T₁ relaxation mechanisms at low temperature. Our results reveal that the VB⁻ center constitutes a strongly coupled electron spin-nuclear spin core, which necessitates the inclusion of the coherent dynamics and derived memory effects of the three nearest-neighbor nitrogen nuclear spins. Using this framework, this work closely reproduces the experimentally observed T₁ time at B = 90\,G and further predicts the T₁ dependence on external magnetic field in the 0 ≤ B ≤ 2000\,G interval, when the spin relaxation is predominantly driven by electron-nuclear and nuclear-nuclear flip-flop processes mediated by hyperfine and dipolar interactions. This study establishes a reliable and scalable approach for describing T₁ relaxation in VB⁻ centers and offers microscopic insights to support future developments in nuclear-spin-based quantum technologies.