Spin-Lattice Interactions in Diamond Quantum Defects: A First-Principles Study of the NV Center

Solid-state spin qubits based on point defects emerge among the proposed platforms for physical qubit implementation due to their long coherence times and optical adressability. The nitrogen-vacancy center in diamond is the most extensively studied example. In this system, spin-spin interactions among the unpaired electrons lift the ground state spin degeneracy, resulting in an energetic separation quantified by the zero-field splitting parameter which enables the identification of a well isolated qubit subsystem. Originating from the interaction between localized electrons, the zero-field splitting is highly sensitive to the atomic structure and its modulation, representing a primary channel for spin-lattice relaxation. It also exhibits a strong dependence on temperature and pressure, forming the basis for sensing applications. Despite extensive studies, the microscopic origin of these dependencies is not fully understood. Their characterization is crucial for engineering spin qubits with controlled decoherence and for the calibration of sensing devices. In this thesis, an ab-initio computational workflow is developed to simulate spin-lattice interactions and compute the temperature and pressure dependence of the zero-field splitting of the nitrogen-vacancy defect. The approach is based on Born-Oppenheimer potential energy surfaces calculated within density functional theory. Structural effects of temperature and pressure are modeled using the quasi-harmonic and stochastic self-consistent harmonic approximations. Thermal and quantum zero-point vibrations are included through ensemble averaging of the zero-field splitting parameter. To overcome the computational cost of anharmonic calculations in large supercells, machine learning interatomic potentials are also employed. The workflow reproduces the experimentally observed trends using both density functional theory and machine learning interatomic potentials. The temperature dependence of the zero-field splitting is reproduced in the range 0 K to 1250 K and is dominated by atomic vibrations rather than thermal expansion. Specifically, below 500 K nuclear quantum vibrations are crucial for quantitative agreement with experiments, while in the range 500 K to 1250 K classical thermal vibrations become dominant. Above 1250 K, the system enters a strongly anharmonic regime where both the quasi-harmonic and the self-consistent harmonic approximations fail. The pressure dependence is in agreement with experiments in the range 0 GPa to 40 GPa and is instead dominated by volumetric compression, while remains unaffected by atomic vibrations. These results contribute to a deeper microscopic understanding of the nitrogen-vacancy center spin-lattice interactions and demonstrate the potential of machine learning methods as powerful tools for quantum materials modeling.