A hybrid method integrating Green’s function Monte Carlo and projected entangled pair states

Abstract

Abstract 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 J 1–J 2 Heisenberg model on a square lattice with periodic boundary conditions (PBCs). 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 [Phys. Rev. B 109 235133 (2024)].