Fermionic tensor network methods

TL;DR

This paper introduces a formalism for incorporating fermionic statistics into tensor network methods using graded Hilbert spaces, enabling local and efficient simulations of fermionic lattice systems without complex transformations.

Contribution

It presents a novel approach to include fermionic statistics in tensor networks via graded Hilbert spaces, simplifying the simulation process and integration with existing methods.

Findings

Fermionic tensor networks can be implemented without Jordan-Wigner transformations.

The formalism integrates smoothly with other symmetries in tensor networks.

Benchmarking shows comparable performance to traditional methods.

Abstract

We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local way, avoiding the need of a Jordan-Wigner transformation or the explicit tracking of leg crossings by swap gates in 2D tensor networks. The graded Hilbert spaces can be readily integrated with other internal and lattice symmetries in tensor networks, and only require minor extensions to an existing tensor network software package. We review and benchmark the fermionic versions of common algorithms for matrix product states and projected entangled-pair states.