Chapter

Entanglement in many-body quantum systems

J. Ignacio Cirac

in Many-Body Physics with Ultracold Gases

Published in print November 2012 | ISBN: 9780199661886
Published online January 2013 | e-ISBN: 9780191748356 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199661886.003.0004

Series: Lecture Notes of the Les Houches Summer School

Entanglement in many-body quantum systems

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This chapter reviews some of the basic concepts coming from the theory of entanglement, their applications to many-body systems, and some of the new theoretical methods that have come up in this context. Section 4.2 and 4.3 introduce entanglement for pure and mixed states, respectively. Two quantities are highlighted: the entropy of entanglement and the quantum mutual information. The first one measures the bipartite entanglement for pure states, whereas the second one measures correlations for both pure and mixed states. Section 4.4 concentrates on many-body states in thermal equilibrium that interact with short-range interactions in lattices. It shows that there is a common property of thermal states in lattice systems with short-range interactions, namely the area law. This fact can guide us in finding an efficient language to describe many-body quantum systems in which the number of parameters only scales polynomially with the number of sites. Under certain conditions, this is indeed possible in terms of so-called tensor network states. Section 4.5 considers how the area law leads to such descriptions and briefly reviews some of them while Section 4.6 concludes.

Keywords: entanglement theory; many-body systems; pure states; mixed states; thermal equilibrium; lattice systems; area law; tensor network states

Chapter.  15052 words.  Illustrated.

Subjects: Atomic, Molecular, and Optical Physics

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