scholarly journals Counterdiabatic route for preparation of state with long-range topological order

2021 ◽  
Vol 104 (24) ◽  
Author(s):  
Sanjeev Kumar ◽  
Shekhar Sharma ◽  
Vikram Tripathi
Keyword(s):  
Long Range ◽  
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.

Long-Range Topological Order in Metallic Glass

Science ◽  
2011 ◽  
Vol 332 (6036) ◽  
pp. 1404-1406 ◽  
Author(s):  
Q. Zeng ◽  
H. Sheng ◽  
Y. Ding ◽  
L. Wang ◽  
W. Yang ◽  
...  
Keyword(s):  
Metallic Glass ◽  
Long Range ◽  
Topological Order

Topological Order in Physics

2017 ◽  
pp. 108-111
Author(s):  
Ravi Karki Karki
Keyword(s):  
Quantum Entanglement ◽  
Long Range ◽  
Mathematical Framework ◽  
Topological Order ◽  
Quantum Numbers ◽  
Light Waves ◽  
Pair Condensation ◽  
Fractional Quantum Numbers ◽  
Solid Liquid ◽  
Zero Viscosity

In general, we know that there are four states of matter solid, liquid, gas and plasma. But there are much more states of matter. For e. g. there are ferromagnetic states of matter as revealed by the phenomenon of magnetization and superfluid states defined by the phenomenon of zero viscosity. The various phases in our colorful world are so rich that it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. Topological phenomena define the topological order at macroscopic level. Topological order need new mathematical framework to describe it. More recently it is found that at microscopic level topological order is due to the long range quantum entanglement, just like the fermions fluid is due to the fermion-pair condensation. Long range quantum entanglement leads to many amazing emergent phenomena, such as fractional quantum numbers, non- Abelian statistics ad perfect conducting boundary channels. It can even provide a unified origin of light and electron i.e. gauge interactions and Fermi statistics. Light waves (gauge fields) are fluctuations of long range entanglement and electron (fermion) are defect of long range entanglements.The Himalayan Physics Vol. 6 & 7, April 2017 (108-111)

scholarly journals A theory of 2+1D bosonic topological orders

2015 ◽  
Vol 3 (1) ◽  
pp. 68-106 ◽  
Author(s):  
Xiao-Gang Wen
Keyword(s):  
Symmetry Breaking ◽  
Long Range ◽  
Tensor Category ◽  
Fusion Category ◽  
Temperature Phase ◽  
Mathematical Framework ◽  
Topological Order ◽  
Spin Qubit ◽  
Crystal Phases ◽  
Solid Liquid

Abstract In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new ‘topological’ phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase—topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems).

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