Matrix Product States with Backflow correlations

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.

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• Thermalization of long range Ising model in different dynamical regimes: a full counting statistics approach
• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Hybrid between biologically and quantum-inspired many-body states