Entanglement entropy for 2D spin lattices

Abstract

This thesis will focus on verifying the area-law for the entanglement entropy SN for spin-1 2 lattice systems in 2 dimensions, with ferromagnetic interactions defined by the nearest neighbour XX-model. The area-law implies that the SN of a subsystem is expected to scale proportionally to the size of the boundary through which that subsystem interacts with the rest of the system. By writing a numerical model in MATLAB, which uses computational devices to circumvent the huge memory requirement that quantum simulations usually demand, it is possible to analyse 2 dimensional systems up to a lattice size of 5 × 5 for the first time. These finite systems have been assigned periodic boundary conditions, as if it were a torus. It doesn’t seem possible to evaluate such systems analytically, unlike 1 dimensional systems, as we will show. The area-law has been shown in a direct way by looking at entanglement entropy, as well as the indirect way by analysing the connected spin correlation.