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 ℤ2 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.
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BibTeX
@misc{usoltcev2026manybody,
title = {{Many-body topology in parity-preserving tensor networks}},
author = {Maksimilian Usoltcev and Nguyen Hanh Dung and Carolin Wille and Matteo Rizzi and Alexander Altland},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40004},
eprint = {2609.40004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40004},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Many-body topology in parity-preserving tensor networks
AU - Maksimilian Usoltcev
AU - Nguyen Hanh Dung
AU - Carolin Wille
AU - Matteo Rizzi
AU - Alexander Altland
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40004
UR - https://arxiv.org/abs/2609.40004
AB - 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 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.
ER -