scholarly journals Experimentally probing topological order and its breakdown through modular matrices

2017 ◽  
Vol 14 (2) ◽  
pp. 160-165 ◽  
Author(s):  
Zhihuang Luo ◽  
Jun Li ◽  
Zhaokai Li ◽  
Ling-Yan Hung ◽  
Yidun Wan ◽  
...  
Keyword(s):  
Topological Order

scholarly journals Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sungmin Kim ◽  
Johannes Schwenk ◽  
Daniel Walkup ◽  
Yihang Zeng ◽  
Fereshte Ghahari ◽  
...  
Keyword(s):  
Atomic Force Microscopy ◽  
Chemical Potential ◽  
Quantum Hall ◽  
Broken Symmetry ◽  
Topological Order ◽  
Edge States ◽  
Force Microscopy ◽  
Atomic Force ◽  
Intimate Relation ◽  
Boundary Measurements

AbstractThe quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the “bulk” topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $${{\nu }}={{0}},\pm {{1}}$$ ν = 0 , ± 1 across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

scholarly journals Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians

2013 ◽  
Vol 111 (9) ◽  
Author(s):  
Norbert Schuch ◽  
Didier Poilblanc ◽  
J. Ignacio Cirac ◽  
David Pérez-García
Keyword(s):  
Transfer Operator ◽  
Topological Order

scholarly journals Reduced density matrices and topological order in a quantum dimer model

2007 ◽  
Vol 19 (14) ◽  
pp. 145212 ◽  
Author(s):  
Shunsuke Furukawa ◽  
Grégoire Misguich ◽  
Masaki Oshikawa
Keyword(s):  
Topological Order ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Dimer Model ◽  
Reduced Density

Polar molecules in topological order

2006 ◽  
Vol 2 (5) ◽  
pp. 309-310 ◽  
Author(s):  
Maciej Lewenstein
Keyword(s):  
Polar Molecules ◽  
Topological Order

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.

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