Many-body topology in parity-preserving tensor networks

Abstract:Planar parity-preserving tensor networks (ppTNs) admit a fermionic formulation in which the Gaussian, efficiently contractible limit is deformed by local interactions. We investigate how many-body methods can be used to analyze such contractions in a minimal two-parameter ppTN. Its contraction is simultaneously an interacting fermionic partition function, a loop gas, a deformed toric-code norm, and a quartic Ising model, allowing the same phase diagram to be approached with complementary tools. At its center lies a `topological island', characterized beyond the Gaussian limit by a boundary-twist $\mathbb Z_2$ indicator that reduces to Chern-number parity and admits a loop-winding interpretation under duality. Fermionic perturbation theory predicts the interacting phase boundaries, tensor-network numerics establish their critical behavior, and the loop and spin descriptions reveal a self-dual line with a $c=1$ four-state-Potts multicritical fixed point.

Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2609.40004 [cond-mat.stat-mech]

(or arXiv:2609.40004v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2609.40004 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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