Corner functions from entanglement indices of harmonic lattices

We study the entanglement indices such as logarithmic negativities (LNs) and mutual informations (MIs) between two adjacent subsets in a isolated universal set $U$ of harmonic oscillators arranged on a two dimensional lattice within a sufficiently large square. First, we verify the values of the corner functions of angle $π/2, π/4, 3π/4$ presented in the previous study which adopts periodic boundary conditions (PBCs) for the $U$. The values of each corner function obtained from LNs are nearly equal to those in the previous ones, while those of $3π/4$ from MIs are not sufficiently consistent with those computed from LNs. Next, for the case where the universal system $U$ satisfies the fixed end boundary conditions(FBCs), we calculate LNs, MIs at several locations in $U$, compare them, especially corner functions with the values obtained in the PBCs case, and examine the effect of the fixed ends. In addition, we examine Renyi entropies for sets of three dimensional lattice sites, the corner functions and the edge terms with solid angles and dihedral angles $π/2,π/4$, respectively.