Sep 14. 2022, 11:45 — 12:30
Tensor network algorithms have proven to be very powerful tools to study 1D and 2D strongly correlated systems. However, their application to 3D quantum systems has so far been limited, mostly because the efficient contraction of a 3D tensor network is very challenging. In this talk I report on recent progress with three different approaches [1, 2]. The first approach is based on a contraction of a finite cluster of tensors including an effective environment to approximate the full 3D network. The second approach performs a full contraction of the network by first iteratively contracting layers of the network with a boundary iPEPS, followed by a contraction of the resulting quasi-2D network using the corner transfer matrix (CTM) method. For the special case of layered systems (i.e. strongly anisotropic models), we propose a contraction scheme in which the weakly-entangled layers are effectively decoupled away from the center of the layers, so that they can be efficiently contracted using 2D contraction methods, while we keep the center of the layers connected in order to capture the most relevant interlayer correlations. Besides benchmark data, I present results for the Shastry-Sutherland model with interlayer coupling, relevant for the layered compound SrCu2(BO3)2.
[1] P. Vlaar and P. Corboz, Phys. Rev. B 103, 205137 (2021).
[2] P. Vlaar and P. Corboz, arxiv:2208.06423