Single-layer framework of variational tensor network states

TL;DR

This paper introduces a single-layer tensor network framework combined with automatic differentiation for efficient variational ground-state calculations in 2D quantum models, achieving high accuracy with reduced computational cost.

Contribution

The authors develop a novel single-layer tensor network approach that significantly reduces computational costs and enables large-scale 2D quantum system simulations.

Findings

Achieved bond dimension of nine with accurate energy estimates.

Confirmed the intermediate valence bond solid phase in the Shastry-Sutherland model.

Reduced computational cost by three orders of magnitude compared to previous methods.

Abstract

We propose a single-layer tensor network framework for the variational determination of ground states in two-dimensional quantum lattice models. By combining the nested tensor network method [Phys. Rev. B 96, 045128 (2017)] with the automatic differentiation technique, our approach can reduce the computational cost by three orders of magnitude in bond dimension, and therefore enables highly efficient variational ground-state calculations. We demonstrate the capability of this framework through two quantum spin models: the antiferromagnetic Heisenberg model on a square lattice and the frustrated Shastry-Sutherland model. Even without GPU acceleration or symmetry implementation, we have achieved a bond dimension of nine and obtained accurate ground-state energy and consistent order parameters compared to prior studies. In particular, we confirm the existence of an intermediate empty-plaquette valence bond solid ground state in the Shastry-Sutherland model. We have further discussed the convergence of the algorithm and its potential improvements. Our work provides a promising route for large-scale tensor network calculations of two-dimensional quantum systems.