Beyond Boundaries: efficient Projected Entangled Pair States methods for periodic quantum systems

TL;DR

This paper introduces an efficient PEPS method for periodic quantum systems by superposing open boundary PEPS, reducing computational costs while maintaining accuracy and broadening applicability to various boundary conditions.

Contribution

The authors develop a novel superposition approach of open boundary PEPS to effectively simulate systems with periodic boundary conditions, overcoming computational limitations.

Findings

Accurately models large periodic systems with reduced computational complexity.

Demonstrates effectiveness on Heisenberg and J1-J2 models.

Applicable to cylindrical and twisted boundary conditions.

Abstract

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 (PBC), 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 (OBC) to treat systems with PBC. This approach significantly reduces the computational complexity of such systems while maintaining their translational invariance and the PBC. 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. The techniques are adaptable to other boundary conditions, including cylindrical and twisted boundary conditions, and therefore significantly expands the application scope of the PEPS approach, shining new light on numerous applications.