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

Zheng Liu, Shiwei Zhang, Fengjie Ma

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.

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

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.
Paper Structure (11 sections, 37 equations, 3 figures, 1 table)

This paper contains 11 sections, 37 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. METHODOLOGY
  3. Hamiltonian
  4. Pseudopotentials
  5. AFQMC with SOC
  6. Propagation
  7. Measurement
  8. APPLICATIONS
  9. I_2 and Pb
  10. Transition pressure of InP
  11. SUMMARY

Figures (3)

  • Figure 1: Dissociation energy of molecule I_2 from SR (labeled "no SOC") and FR (labeled "with SOC") calculations, comparing the results from DFT-LDA (gray bins), phaseless pw-AFQMC (blue bins) and experiment (orange bins). Statistical uncertainties for the phaseless pw-AFQMC calculations are represented by black horizontal error bars.
  • Figure 2: Cohesive energy of bulk Pb. DFT-LDA and phaseless pw-AFQMC results are displayed as gray and blue bins, respectively. Finite-size correction has been applied to the phaseless pw-AFQMC results. The orange bin with an error bar represents the experimental value with its associated uncertainty. Black horizontal bars on blue bins represent the stochastic uncertainties of the phaseless pw-AFQMC calculations.
  • Figure 3: Equation of state curves for ZB (black solid lines) and RS (blue solid lines) phases of InP (fitted to the third-order Birch-Murnaghan equation). Filled circles (ZB) and squares (RS) correspond to the calculated data from phaseless pw-AFQMC, with the associated stochastic errors being smaller than the marker size. All values, obtained using cubic supercell, are converted to the one-formula primitive cell for consistency in presentation. The red dashed line denotes the common tangent to the two EOS curves and its (negative) slope represents the transition pressure $P_t$, where the value in parentheses denotes the statistical error during fittings. Arrows indicate the direction of residual finite-size errors, as discussed in the main text.