Fermionic tensor network methods
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 the use of 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, 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.
Authors
- Frank Verstraete (ORCID: https://orcid.org/0000-0003-0270-5592)
- Nick Bultinck (ORCID: https://orcid.org/0000-0002-2781-4085)
- Quinten Mortier (ORCID: https://orcid.org/0000-0003-3781-7869)
- Bram Vanhecke (ORCID: https://orcid.org/0000-0001-9557-1591)
- Jutho Haegeman (ORCID: https://orcid.org/0000-0002-0858-291X)
- Lukas Devos
- Lander Burgelman (ORCID: https://orcid.org/0000-0003-1724-5330)
- Laurens Vanderstraeten (ORCID: https://orcid.org/0000-0002-3227-9822)
Institutions
- University of Vienna (AT)
- Université Libre de Bruxelles (BE)
- University of Cambridge (GB)
- Ghent University Hospital (BE)
Publication Details
- Journal
- SciPost Physics
- Published
- 2025-01-10
- DOI
- https://doi.org/10.21468/scipostphys.18.1.012
- Citations
- 11
- Primary Topic
- Quantum many-body systems
- Type
- article
- Field-Weighted Citation Impact
- 13.71
Funders
- Fonds De La Recherche Scientifique - FNRS
- Fonds Wetenschappelijk Onderzoek
- Vlaamse regering
- Horizon 2020