A minimal tensor network beyond free fermions

• URL: http://arxiv.org/abs/2412.04216v1
• Date: Thu, 05 Dec 2024 14:49:39 GMT
• Title: A minimal tensor network beyond free fermions
• Authors: Carolin Wille, Maksimilian Usoltcev, Jens Eisert, Alexander Altland,
• Abstract summary: This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems. 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. The resulting model is simple, featuring only two parameters: one governing spin-spin interaction and the other measuring the deviation from the free fermion limit.
• Score: 39.847063110051245
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• Abstract: 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 tricritical 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.

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