Excitation gap of a blockade structure with $\mathbb{Z}_2$ topological order

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.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph)

arXiv:2609.39475 [quant-ph]

(or arXiv:2609.39475v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.39475 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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