This paper introduces a hybrid approach combining Green's function Monte Carlo (GFMC) method with projected entangled pair state (PEPS) ansatz. This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC. By leveraging PEPS's proficiency in capturing quantum state entanglement and GFMC's efficient parallel architecture, the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems. As a benchmark, we applied this approach to study the frustrated J1-J2 Heisenberg model on a square lattice with periodic boundary conditions (PBC). Compared with other numerical methods, our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy. This paper provides systematic and comprehensive discussion of the approach of our previous work.
@article{arxiv.2503.08450,
title = {A hybrid method integrating Green's function Monte Carlo and projected entangled pair states},
author = {He-Yu Lin and Rong-Qiang He and Yibin Guo and Zhong-Yi Lu},
journal= {arXiv preprint arXiv:2503.08450},
year = {2025}
}