Tensor network representations from the geometry of entangled states

TL;DR

This paper introduces a geometric approach to constructing tensor network representations that reduce effective bond dimension, enhancing the efficiency of modeling complex entangled quantum states like the resonating valence bond state on kagome lattices.

Contribution

The authors develop a method leveraging the geometry of entangled states to create tensor networks with smaller effective bond dimensions, applicable to complex quantum systems.

Findings

Method reduces effective bond dimension in tensor networks.

Application to resonating valence bond states on kagome lattice.

Improved efficiency in representing strongly correlated quantum states.

Abstract

Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement structure given by a graph of maximally entangled states along the edges that identify the indices of the tensors to be contracted. Recently, more general tensor networks have been considered, where the maximally entangled states on edges are replaced by multipartite entangled states on plaquettes. Both the structure of the underlying graph and the dimensionality of the entangled states influence the computational cost of contracting these networks. Using the geometrical properties of entangled states, we provide a method to construct tensor network representations with smaller effective bond dimension. We illustrate our method with the resonating valence bond state on the kagome lattice.