Fermionic Orbital Optimization in Tensor Network States

Krumnow, C. and Veis, L. and Legeza, Örs and Eisert, J. (2016) Fermionic Orbital Optimization in Tensor Network States. PHYSICAL REVIEW LETTERS, 117 (21). ISSN 0031-9007

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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.

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