Energy bonds as correlators for long-range symmetry-protected topological models and models with long-range topological order

2020 ◽  
Vol 101 (24) ◽  
Author(s):  
Wing Chi Yu ◽  
Chen Cheng ◽  
P. D. Sacramento
Keyword(s):  
Long Range ◽  
Topological Order ◽  
Symmetry Protected ◽  
Topological Models

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

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Xiao-Gang Wen
Keyword(s):  
Symmetry Breaking ◽  
Long Range ◽  
Topological Order ◽  
Fractional Statistics ◽  
Microscopical Level ◽  
Macroscopic Level ◽  
Emergent Phenomena ◽  
Quantum Matter ◽  
Ordered Phases ◽  
Zero Viscosity

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.

scholarly journals Detecting subsystem symmetry protected topological order via entanglement entropy

2019 ◽  
Vol 100 (11) ◽  
Author(s):  
David T. Stephen ◽  
Henrik Dreyer ◽  
Mohsin Iqbal ◽  
Norbert Schuch
Keyword(s):  
Entanglement Entropy ◽  
Topological Order ◽  
Symmetry Protected

scholarly journals Many-body localization and symmetry-protected topological order

2014 ◽  
Vol 89 (14) ◽  
Author(s):  
Anushya Chandran ◽  
Vedika Khemani ◽  
C. R. Laumann ◽  
S. L. Sondhi
Keyword(s):  
Topological Order ◽  
Many Body ◽  
Symmetry Protected

scholarly journals U(1)×U(1)symmetry-protected topological order in Gutzwiller wave functions

2014 ◽  
Vol 90 (23) ◽  
Author(s):  
Zheng-Xin Liu ◽  
Jia-Wei Mei ◽  
Peng Ye ◽  
Xiao-Gang Wen
Keyword(s):  
Wave Functions ◽  
Topological Order ◽  
Symmetry Protected
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