2020/10/07 by Wenhan Guo, Guo, Wenhan, Nicholas Pomata +3
Physics and Astronomy · #Advanced Condensed Matter Physics #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2010.03137
openalex publication_date 2020/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently various 2D AKLT models have been shown to be gapped, including the one on the hexagonal lattice. Here we report on a non-trivial 3D AKLT model which consists of spin-2 entities on the diamond lattice sites and one single spin-1 entity between every neighboring spin-2 site. Although the nonzero gap problem for the uniformly spin-2 AKLT models on the diamond and square lattices is still open, we are able to establish the existence of the gap for two planar lattices, which we call the inscribed square lattice and the triangle-octagon lattice, respectively. So far, these latter two models are the only two uniformly spin-2 AKLT models that have a provable nonzero gap above the ground state. We also discuss some attempts in proving the gap existence on both the square and kagome lattices. In addition, we show that if one can solve a finite-size problem of a weighted AKLT Hamiltonian and if the gap is larger than certain threshold, then the model on the square lattice is gapped in the thermodynamic limit. The threshold of the gap scales inversely with the linear size of the finite-size problem.