6 problems

Consider the AKLT models on the two-dimensional honeycomb lattice and the two-dimensional square lattice, defined by nearest-neighbor AKLT interactions with the corresponding latti…

Consider the AKLT state, whose configurations in the Ising basis obey diluted Néel order: between any two $+$ spins there is a $-$ spin and between any two $-$ spins there is a $+$…

The AKLT model is a quantum spin model whose ground states are the lowest-energy states of its Hamiltonian. A state has antiferromagnetic long-range order when spin correlations ex…

Let $\Gamma$ be a lattice with $\deg(x)=d$ at each site $x\in\Gamma$, with a spin-$s=d/2$ particle at each site. For nearest-neighbor sites, define the AKLT interaction by … where…

Let the hexagonal-lattice AKLT model have spin $S=3/2$ at each site, with its valence-bond-solid ground state. A spectral gap means a strictly positive separation between the groun…

Vanishing-negativity conjecture. The negativity between the two non-adjacent blocks vanishes for every value of the spin $S$.