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PreprintarXiv licencearXiv

Excitation gap of a blockade structure with ℤ2 topological order

  • Simon Fell
  • Tobias F. Maier
  • Hans Peter Büchler
  • Nicolai Lang
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Abstract

Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove -- yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.

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Cite

BibTeXRIS
BibTeX
@misc{fell2026excitation,
  title = {{Excitation gap of a blockade structure with $\mathbbZ_2$ topological order}},
  author = {Simon Fell and Tobias F. Maier and Hans Peter Büchler and Nicolai Lang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39475},
  eprint = {2609.39475},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39475},
}
RIS
TY  - UNPB
TI  - Excitation gap of a blockade structure with ℤ_2 topological order
AU  - Simon Fell
AU  - Tobias F. Maier
AU  - Hans Peter Büchler
AU  - Nicolai Lang
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39475
UR  - https://arxiv.org/abs/2609.39475
AB  - Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove -- yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.
ER  -