Efficient tensor network algorithm for layered systems

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 Néel 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.

arXiv comment7 pages, 5 figures, 6 pages of supplemental material

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• Tensor network study of the Shastry-Sutherland model with weak interlayer coupling
• Single-layer tensor network approach for three-dimensional quantum systems
• Exploiting the Hermitian symmetry in tensor network algorithms