Print Email Facebook Twitter Entanglement entropy for 2D spin lattices Title Entanglement entropy for 2D spin lattices Author Ivlev, Sasha (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Visser, Paul (mentor) Blanter, Yaroslav (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics | Applied Physics Date 2019-07-11 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. Subject EntanglementEntropyQuantumSpin lattice To reference this document use: http://resolver.tudelft.nl/uuid:5a8b0aff-e9b7-4f9f-ba2d-6d809954dcff Embargo date 2019-11-13 Part of collection Student theses Document type bachelor thesis Rights © 2019 Sasha Ivlev Files PDF Alexander_Ivlev_BEP.pdf 2.39 MB Close viewer /islandora/object/uuid:5a8b0aff-e9b7-4f9f-ba2d-6d809954dcff/datastream/OBJ/view