Spin-orbit coupling (SOC) is incorporated into the phaseless plane-wave-based auxiliary-field quantum Monte Carlo (pw-AFQMC) method. This integration is implemented using optimized multiple-projector norm-conserving pseudopotentials, which are derived from the fully relativistic (FR) atomic all-electron Dirac-like equation. The inclusion of SOC enables accurate phaseless pw-AFQMC calculations that capture both electronic correlation and SOC effects concurrently, greatly improving the applicability of the method to studying systems containing heavy atoms. We discuss the form of FR pseudopotentials and detail the corresponding formulations of phaseless pw-AFQMC with a two-component Hamiltonian in the spinor basis. The accuracy of our approach is demonstrated by computing the dissociation energy of molecule ${\mathrm{I}}_2$ and the cohesive energy of bulk Pb, highlighting the large influence of SOC in both. Subsequently, we determine the transition pressure of the III-V compound InP from its zinc-blende to rock-salt phase by constructing and analyzing their respective equations of state.

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• Electronic structure
• First-principles calculations
• Many-body techniques
• Plane-wave expansion
• Quantum Monte Carlo