Phaseless auxiliary-field quantum Monte Carlo method with spin-orbit coupling

TL;DR

This paper extends the phaseless auxiliary-field quantum Monte Carlo method to include spin-orbit coupling, enabling accurate simulations of heavy-atom systems by capturing electronic correlation and SOC effects simultaneously.

Contribution

The integration of spin-orbit coupling into the phaseless pw-AFQMC method using optimized relativistic pseudopotentials is a novel advancement.

Findings

Accurate dissociation energy of I2 computed with SOC included.

Cohesive energy of bulk Pb calculated demonstrating SOC effects.

Transition pressure of InP from zinc-blende to rock-salt phase determined.

Abstract

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 method's applicability for 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 I2 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.