Ground-state spaces of generalized stabilizer codes

Abstract

In this paper, we determine the complete ground-state spaces for a broad class of generalized stabilizer quantum models defined over CW-decompositions of non-compact manifolds of arbitrary dimensions and topological type. We introduce a C^*-algebraic framework in which the quantum spin algebra A is realized as the twisted group C^*-algebra of an infinite discrete Pauli module P endowed with a symplectic structure. We establish a correspondence between stabilizer models and isotropic subgroups of P: Every Lagrangian extension of such a subgroup determines a C^*-diagonal of A, whose Weyl groupoid encodes the dynamics through a continuous 1-cocycle. This realization yields an explicit family of extremal ground-states for every admissible Lagrangian model, together with their decomposition into sectors. When the sector space is T₀, this gives a complete characterization of the ground-state spaces. We also prove that every Lagrangian stabilizer model admits a unique frustration-free ground state with a spectral gap. Our framework applies in arbitrary dimension, including higher abelian quantum doubles, homological codes, and a broad class of stabilizer models.

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BibTeX RIS

BibTeX

@misc{cheng2026groundstate,
  title = {{Ground-state spaces of generalized stabilizer codes}},
  author = {Cathy Cheng and Nigel Higson and Danilo Polo Ojito and Emil Prodan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33221},
  eprint = {2610.33221},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33221},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Ground-state spaces of generalized stabilizer codes
AU  - Cathy Cheng
AU  - Nigel Higson
AU  - Danilo Polo Ojito
AU  - Emil Prodan
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33221
UR  - https://arxiv.org/abs/2610.33221
AB  - In this paper, we determine the complete ground-state spaces for a broad class of generalized stabilizer quantum models defined over CW-decompositions of non-compact manifolds of arbitrary dimensions and topological type. We introduce a C^*-algebraic framework in which the quantum spin algebra A is realized as the twisted group C^*-algebra of an infinite discrete Pauli module P endowed with a symplectic structure. We establish a correspondence between stabilizer models and isotropic subgroups of P: Every Lagrangian extension of such a subgroup determines a C^*-diagonal of A, whose Weyl groupoid encodes the dynamics through a continuous 1-cocycle. This realization yields an explicit family of extremal ground-states for every admissible Lagrangian model, together with their decomposition into sectors. When the sector space is T_0, this gives a complete characterization of the ground-state spaces. We also prove that every Lagrangian stabilizer model admits a unique frustration-free ground state with a spectral gap. Our framework applies in arbitrary dimension, including higher abelian quantum doubles, homological codes, and a broad class of stabilizer models.
ER  -

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