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Topological Entanglement Entropy

Kitaev, Alexei and Preskill, John (2006) Topological Entanglement Entropy. Physical Review Letters, 96 (11). Art. No. 110404. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:KITprl06

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Abstract

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho)=alphaL-gamma+[centered ellipsis], where the ellipsis represents terms that vanish in the limit L-->[infinity]. We show that -gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.


Item Type:Article
Additional Information:©2006 The American Physical Society (Received 13 October 2005; published 24 March 2006) We thank Anton Kapustin for discussions. This work has been supported in part by: the Department of Energy under Grant No. DE-FG03-92-ER40701, the National Science Foundation under Grant No. PHY-0456720, the Army Research Office under Grants No. W911NF-04-1-0236 and No. W911NF-05-1-0294, and the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374.
Subject Keywords:quantum entanglement; quantum field theory; ground states; entropy; many-body problems; fermion systems
Record Number:CaltechAUTHORS:KITprl06
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KITprl06
Alternative URL:http://dx.doi.org/10.1103/PhysRevLett.96.110404
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3504
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:09 Jun 2006
Last Modified:18 Sep 2014 18:11

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