Matrix Product States with Backflow correlations

TL;DR

This paper introduces a novel tensor network ansatz inspired by backflow transformations, extending Matrix Product States to better capture entanglement in quantum many-body systems, and demonstrates its effectiveness on spin models.

Contribution

The paper presents a new tensor network ansatz incorporating backflow correlations, enhancing the ability to model entanglement and improve ground-state searches in quantum systems.

Findings

Achieves high accuracy in 1D and 2D spin models.

Effectively studies the 2D $J_1 - J_2$ model.

Competitive with state-of-the-art methods in 2D.

Abstract

By taking inspiration from the backflow transformation for correlated systems, we introduce a novel tensor network ansatz which extend the well-established Matrix Product State representation of a quantum-many body wave function. This new structure provides enough resources to ensure that states in dimension larger or equal than one obey an area law for entanglement. It can be efficiently manipulated to address the ground-state search problem by means of an optimization scheme which mixes tensor-network and variational Monte-Carlo algorithms. We benchmark the new ansatz against spin models both in one and two dimensions, demonstrating high accuracy and precision. We finally employ our approach to study the challenging $S=1/2$ two dimensional $J_1 - J_2$ model, demonstrating that it is competitive with the state of the art methods in 2D.