TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.1.012
TI  - Fermionic tensor network methods
PY  - 2025/01/10
UR  - https://scipost.org/SciPostPhys.18.1.012
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 1
SP  - 012
A1  - Mortier, Quinten
AU  - Devos, Lukas
AU  - Burgelman, Lander
AU  - Vanhecke, Bram
AU  - Bultinck, Nick
AU  - Verstraete, Frank
AU  - Haegeman, Jutho
AU  - Vanderstraeten, Laurens
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.1.012,
	title={{Fermionic tensor network methods}},
	author={Quinten Mortier and Lukas Devos and Lander Burgelman and Bram Vanhecke and Nick Bultinck and Frank Verstraete and Jutho Haegeman and Laurens Vanderstraeten},
	journal={SciPost Phys.},
	volume={18},
	pages={012},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.1.012},
	url={https://scipost.org/10.21468/SciPostPhys.18.1.012},
}