Exact Calculation of Entanglement in a 19-site 2D Spin System

• Published in: arXiv.org
• Main Authors: Xu, Qing, Kais, Sabre, Naumov, Maxim, Ahmed, Sameh
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 13.01.2010
• Subjects: Absolute zero; Algorithms; Entanglement; Ising model; Particle spin; Phase transitions; Physics - Quantum Physics; Quantum phenomena; Two dimensional models
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0909.4764

Using the Trace Minimization Algorithm, we carried out an exact calculation of entanglement in a 19-site two-dimensional transverse Ising model. This model consists of a set of localized spin-1/2 particles in a two dimensional triangular lattice coupled through exchange interaction J and subject to an external magnetic field of strength h. We demonstrate, for such a class of two-dimensional magnetic systems, that entanglement can be controlled and tuned by varying the parameter \(\lambda\) = h/J in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of \(\lambda\) shows that the system exhibits a quantum phase transition at about \(\lambda_c\) = 3.01, a transition induced by quantum fluctuations at the absolute zero of temperature.