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ISRN Condensed Matter Physics
Volume 2013 (2013), Article ID 198710, 20 pages
http://dx.doi.org/10.1155/2013/198710
Review Article

Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons

1Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada N2L 2Y5
2Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
3Institute for Advanced Study, Tsinghua University, Beijing 100084, China

Received 2 October 2012; Accepted 19 November 2012

Academic Editors: H. Eisaki, C. Janowitz, C. Trallero-Giner, and T. Yanagisawa

Copyright © 2013 Xiao-Gang Wen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We review the progress in the last 20–30 years, during which we discovered that there are many new phases of matter that are beyond the traditional Landau symmetry breaking theory. We discuss new “topological” phenomena, such as topological degeneracy that reveals the existence of those new phases—topologically ordered phases. Just like zero viscosity defines the superfluid order, the new “topological” phenomena define the topological order at macroscopic level. More recently, we found that at the microscopical level, topological order is due to long-range quantum entanglements. Long-range quantum entanglements lead to many amazing emergent phenomena, such as fractional charges and fractional statistics. Long-range quantum entanglements can even provide a unified origin of light and electrons; light is a fluctuation of long-range entanglements, and electrons are defects in long-range entanglements.