Fine-Grained Tensor Network Methods

TL;DR

This paper introduces a tensor network approach that simplifies high-connectivity lattices by fine-graining degrees of freedom, enabling efficient simulation of complex quantum models with improved accuracy over existing methods.

Contribution

The authors propose a novel fine-graining strategy for tensor networks that transforms complex lattices into simpler structures, facilitating more efficient and accurate simulations.

Findings

Successfully applied to spin-1 transverse-field Ising model on triangular lattices

Achieved accurate results for Bose-Hubbard models on triangular lattices

Demonstrated improved performance over existing techniques

Abstract

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse-graining, provide the original ones. Thanks to this procedure, the original lattice with high connectivity is transformed by an isometry into a simpler structure, which is easier to simulate via usual tensor network methods. In particular this enables the use of standard schemes to contract infinite 2d tensor networks - such as Corner Transfer Matrix Renormalization schemes - which are more involved on complex lattice structures. We prove the validity of our approach by numerically computing the ground-state properties of the ferromagnetic spin-1 transverse-field Ising model on the 2d triangular and 3d stacked triangular lattice, as well as of the hard-core and soft-core Bose-Hubbard models on the triangular lattice. Our results are benchmarked against those obtained with other techniques, such as perturbative continuous unitary transformations and graph projected entangled pair states, showing excellent agreement and also improved performance in several regimes.