Corner functions from entanglement indices of harmonic lattices

TL;DR

This paper investigates entanglement measures like logarithmic negativity and mutual information in harmonic lattices, analyzing corner functions under different boundary conditions and comparing their behaviors.

Contribution

It provides a detailed comparison of corner functions from entanglement indices in harmonic lattices with different boundary conditions, extending previous studies.

Findings

Corner functions from LNs are consistent with previous results.

MIs corner functions for 3π/4 are less consistent with LNs.

Boundary conditions significantly affect entanglement measures.

Abstract

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 $\pi/2, \pi/4, 3\pi/4$ 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 $3\pi/4$ 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 $\pi/2,\pi/4$, respectively.