Efficient tensor network algorithm for layered systems

TL;DR

This paper introduces an efficient tensor network algorithm based on iPEPS for layered 2D systems, enabling accurate simulations of complex strongly correlated materials that are challenging for traditional methods.

Contribution

The authors develop a novel contraction scheme for layered 2D systems using anisotropic 3D iPEPS, improving computational efficiency and accuracy in capturing interlayer correlations.

Findings

Benchmark results agree with QMC and 3D contraction data.

Effective decoupling scheme reduces computational complexity.

Applied to frustrated spin models beyond QMC capabilities.

Abstract

Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an efficient tensor network approach based on infinite projected entangled-pair states (iPEPS) for layered 2D systems. Starting from an anisotropic 3D iPEPS ansatz, we propose a contraction scheme in which the weakly-interacting layers are effectively decoupled away from the center of the layers, such that they can be efficiently contracted using 2D contraction methods while keeping the center of the layers connected in order to capture the most relevant interlayer correlations. We present benchmark data for the anisotropic 3D Heisenberg model on a cubic lattice, which shows close agreement with quantum Monte Carlo (QMC) and full 3D contraction results. Finally, we study the dimer to N\'eel phase transition in the Shastry-Sutherland model with interlayer coupling, a frustrated spin model which is out of reach of QMC due to the negative sign problem.