Work

Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices

Year: 2026

Type: article

Abstract: We prove that the ground state of the AKLT models on the hexagonal lattice and the Lieb lattice satisfy the local topological quantum order (LTQO) condition. This will be a consequence of proving that the finite volume ground states are indistinguishable from a unique infinite volume ground state. Concretely, we identify a sequence of increasing and absorbing finite volumes for which any finite volume ground state expectation is well approximated by the infinite volume state with error decaying at a uniform exponential rate in the distance between the support of the observable and boundary of the finite volume. As a corollary to the LTQO property, we obtain that the spectral gap above the ground state in these models is stable under general small perturbations of sufficient decay. We prove these results by a detailed analysis of the polymer representation of the ground states state derived by Kennedy et al. [34] with the necessary modifications required for proving the strong form of ground state indistinguishability needed for LTQO.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-026-05752-9

Authors: Thomas Jackson, Bruno Nachtergaele, Amanda Young

Institutions: United Arab Emirates University, University of California, Davis, University of Illinois Urbana-Champaign

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: National Science Foundation