Direct Computation of Berry Phase and Polarizations in Solids by Auxiliary Field Quantum Monte Carlo

We present a direct, ab initio computation of Berry phases with auxiliary field quantum Monte Carlo (AFQMC). AFQMC has shown to be an excellent total energy method, and gradients such as forces and stress can now be computed in solids [1]. With an improved correlated sampling algorithm [2], we propose a method that allows the calculation of Berry phases and polarizations. We demonstrate the accuracy of the method in the Hubbard dimer model system and real solids. This development paves the path for an ab initio many-body approach to directly compute electric and topological properties in periodic systems.

[1] S. Chen and S. Zhang, Phys. Rev. B 107, 195150 (2023)

[2] S. Chen, Y. Yang, M. A. Morales, and S. Zhang, arXiv: 2307.15203