scholarly journals Hidden symmetry-breaking picture of symmetry-protected topological order

2013 ◽  
Vol 88 (8) ◽  
Author(s):  
Dominic V. Else ◽  
Stephen D. Bartlett ◽  
Andrew C. Doherty
Keyword(s):  
Symmetry Breaking ◽  
Topological Order ◽  
Hidden Symmetry ◽  
Symmetry Protected

scholarly journals Choreographed entanglement dances: Topological states of quantum matter

Science ◽  
2019 ◽  
Vol 363 (6429) ◽  
pp. eaal3099 ◽  
Author(s):  
Xiao-Gang Wen
Keyword(s):  
Symmetry Breaking ◽  
Emergent Properties ◽  
Topological Phases ◽  
Topological Order ◽  
Zero Temperature ◽  
Quantum Matter ◽  
Topological States ◽  
Basic Concepts ◽  
Symmetry Protected

It has long been thought that all different phases of matter arise from symmetry breaking. Without symmetry breaking, there would be no pattern, and matter would be featureless. However, it is now clear that for quantum matter at zero temperature, even symmetric disordered liquids can have features, giving rise to topological phases of quantum matter. Some of the topological phases are highly entangled (that is, have topological order), whereas others are weakly entangled (that is, have symmetry-protected trivial order). This Review provides a brief summary of these zero-temperature states of matter and their emergent properties, as well as their importance in unifying some of the most basic concepts in nature.

scholarly journals Unsplit superconducting and time reversal symmetry breaking transitions in Sr2RuO4 under hydrostatic pressure and disorder

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Vadim Grinenko ◽  
Debarchan Das ◽  
Ritu Gupta ◽  
Bastian Zinkl ◽  
Naoki Kikugawa ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Symmetry Breaking ◽  
Time Reversal ◽  
Order Parameter ◽  
Muon Spin Rotation ◽  
Horizontal Line ◽  
Time Reversal Symmetry ◽  
Zero Field ◽  
Symmetry Protected ◽  
Line Node

AbstractThere is considerable evidence that the superconducting state of Sr2RuO4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, TTRSB, is generally found to match the critical temperature, Tc, within resolution. In combination with evidence for even parity, this result has led to consideration of a dxz ± idyz order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding TTRSB = Tc, but it has a hard-to-explain horizontal line node at kz = 0. Therefore, s ± id and d ± ig order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain TTRSB ≈ Tc. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr2RuO4 under hydrostatic pressure, and Sr1.98La0.02RuO4 at zero pressure. Both hydrostatic pressure and La substitution alter Tc without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, TTRSB should track changes in Tc, while if it is accidental, these transition temperatures should generally separate. We observe TTRSB to track Tc, supporting the hypothesis of dxz ± idyz 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.

scholarly journals Parafermionic phases with symmetry breaking and topological order

2016 ◽  
Vol 94 (12) ◽  
Author(s):  
A. Alexandradinata ◽  
N. Regnault ◽  
Chen Fang ◽  
Matthew J. Gilbert ◽  
B. Andrei Bernevig
Keyword(s):  
Symmetry Breaking ◽  
Topological Order

scholarly journals Observation of fractional Chern insulators in a van der Waals heterostructure

Science ◽  
2018 ◽  
Vol 360 (6384) ◽  
pp. 62-66 ◽  
Author(s):  
Eric M. Spanton ◽  
Alexander A. Zibrov ◽  
Haoxin Zhou ◽  
Takashi Taniguchi ◽  
Kenji Watanabe ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Boron Nitride ◽  
Symmetry Breaking ◽  
Hexagonal Boron Nitride ◽  
Landau Levels ◽  
Topological Order ◽  
Hall Conductance ◽  
Van Der Waals Heterostructure ◽  
Ordered Phases ◽  
Chern Insulators

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene–hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices C=−1, ±2, and ±3. Some of these phases, in C=−1 and C=2 bands, are characterized by fractional Hall conductance—that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.

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
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