Entanglement of valence-bond-solid state models on topological surfaces - Wuttichai Pankeaw; Pruet Kalasuwan; Teparksorn Pengpan (Results in Physics, 2022)
We investigated the scaling behaviors of entanglements on the two-leg ladder lattice structure implemented with Affleck–Kennedy–Lieb–Tasaki (AKLT) model on six types of topological surfaces, namely, torus, sphere, real projective plane, Klein bottle, cylinder and Möbius strip. All six topological surfaces on which our lattices were embedded are classified according to whether their boundaries are closed or open. Lattice structures on these topological surfaces are formed either by a trivalent or four-valent site to fulfill a complete spin-32or spin-2 system, respectively. Their ground states, which are the valence-bond-solid states, are derived by the tensor-product method. The von Neumann entropies for entanglement of the bipartite region on all six topological surfaces are calculated and all results show that the entanglement entropies per area are bounded from above or below when approaching the thermodynamic limit. For the spin-2 and the spin-32systems on all surfaces, except on the sphere, numerical results between even and odd cases of the number of lattice sites should be considered separately for scrutinizing their scaling behaviors. However, their entanglement entropies still satisfy the area law, but with a correction term.