Revision 1

Accepted · first revision · record

Title: Spectral gap of the AKLT model on the square lattice
Plain: The AKLT model is a specially designed quantum magnet whose ground state is known exactly. Its energy gap is proven in one dimension and on the honeycomb lattice but not on the square lattice.
Precise: Spin-2 AKLT model on $Z^{2}$: H = sum_<ij> P^(4)_{ij}, with P^(4) the projector onto total spin 4 of a nearest-neighbour pair. Prove that the gap above the unique ground state is bounded below uniformly in system size. Answer: a proof, possibly via a finite-size criterion checked by computer.
Settled by: A finite-size gap criterion verified numerically with rigorous error control, or an analytic proof.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: open
Status note: Gaps are proven on the hexagonal lattice (Lemm, Sandvik and Wang; Pomata and Wei, 2019-2020) and on decorated square lattices (2019), extended to generalized decorated graphs (Lucia and Young, 2023) and other spin-2 lattices (Guo, Pomata and Wei, 2021); the undecorated square lattice remains unproven.
Posed since: 1987