Matrix product states with backflow correlations

By taking inspiration from the backflow transformation for correlated systems, we introduce a tensor network Ansatz which extends the well-established matrix product state representation of a quantum many-body wave function. This structure provides enough resources to ensure that states in dimensions larger than or equal to 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 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 (2D) J(1) -J(2) model, that it is with the state-of-the-art methods in 2D.

Automated summary

By introducing backflow transformation and tensor network Ansatz, this study extends the matrix product state representation of a quantum many-body wave function and provides enough resources to ensure that states in dimensions larger than or equal to one follow the area law for entanglement. The optimization scheme that combines tensor network and variational Monte Carlo algorithms efficiently addresses the ground-state search problem and demonstrates high accuracy and precision in spin models.