Fermionic orbital optimisation in tensor network states

TL;DR

This paper introduces a method to optimize fermionic orbitals within tensor network states, enhancing the simulation of strongly correlated fermionic systems by combining matrix product state optimization with fermionic Gaussian mode transformations.

Contribution

It presents a novel algorithm that generalizes basis changes akin to Hartree-Fock to tensor network states, enabling automated orbital optimization in fermionic simulations.

Findings

Algorithm effectively optimizes fermionic orbitals in tensor networks.

Improves accuracy of ground state simulations for fermionic systems.

Provides a black box tool for basis optimization in tensor network methods.

Abstract

Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in the context of quantum chemistry. A new freedom arising in such non-local fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this work, we propose a way to overcome this challenge. We suggest a method intertwining the optimisation over matrix product states with suitable fermionic Gaussian mode transformations. The described algorithm generalises basis changes in the spirit of the Hartree-Fock method to matrix-product states, and provides a black box tool for basis optimisation in tensor network methods.