TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.6.196
TI  - A minimal tensor network beyond free fermions
PY  - 2025/06/19
UR  - https://scipost.org/SciPostPhys.18.6.196
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 6
SP  - 196
A1  - Wille, Carolin
AU  - Usoltcev, Maksimilian
AU  - Eisert, Jens
AU  - Altland, Alexander
AB  - This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems beyond the case of free fermions. A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the partition sum of a classical statistical mechanics model to a Grassmann variable integral, structurally similar to the path integral for interacting fermions in two dimensions. The resulting model is simple, featuring only two parameters: one governing spin-spin interaction (dual to effective hopping strength in the fermionic picture), the other measuring the deviation from the free fermion limit. Nevertheless, it exhibits a rich phase diagram, partially stabilized by elements of topology, and featuring three phases meeting at a multicritical point. Besides the interpretation as a spin and fermionic system, the model is closely related to loop gas and vertex models and can be interpreted as a parity-preserving (non-unitary) circuit. Its minimal construction makes it an ideal reference system for studying non-linearities in tensor networks and deriving results by means of duality.
ER  -

@Article{10.21468/SciPostPhys.18.6.196,
	title={{A minimal tensor network beyond free fermions}},
	author={Carolin Wille and Maksimilian Usoltcev and Jens Eisert and Alexander Altland},
	journal={SciPost Phys.},
	volume={18},
	pages={196},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.6.196},
	url={https://scipost.org/10.21468/SciPostPhys.18.6.196},
}