Matrix product states with backflow correlations

By taking inspiration from the backflow transformation for correlated systems, we introduce a novel tensor network ansatz which extend well-established Matrix Product State representation of 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 entanglement. It can be efficiently manipulated address ground-state search problem by means optimization scheme mixes tensor-network and variational Monte-Carlo algorithms. We benchmark against spin models both two dimensions, demonstrating high accuracy precision. finally employ our approach study challenging $S=1/2$ dimensional $J_1 - J_2$ model, it is competitive with state art methods 2D.