Efficient Projected Entangled Pair States Methods for Periodic Quantum Systems

Projected entangled pair states (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, a significant challenge emerges when applying conventional PEPS methodologies to systems with periodic boundary conditions (PBCs), attributed to the prohibitive computational scaling with the bond dimension. This has notably restricted the study of systems with complex boundary conditions. To address this challenge, we have developed a strategy that involves the superposition of PEPS with open boundary conditions (OBCs) to treat systems with PBCs. This approach significantly reduces the computational complexity of such systems while maintaining their translational invariance and the PBCs. We benchmark this method against the Heisenberg model and the J_{1}-J_{2} model, demonstrating its capability to yield highly accurate results at low computational costs, even for large system sizes. We further apply the method to study the Chern numbers of the hard-core Harper-Hofstadter model at different filling factors using twisted boundary conditions. This advancement significantly broadens the applicability of the PEPS approach, opening new avenues for studying a wide range of quantum many-body phenomena.