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 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 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 Confinement transition of ℤ2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry

2018 ◽  
Vol 115 (30) ◽  
pp. E6987-E6995 ◽  
Author(s):  
Snir Gazit ◽  
Fakher F. Assaad ◽  
Subir Sachdev ◽  
Ashvin Vishwanath ◽  
Chong Wang
Keyword(s):  
Monte Carlo ◽  
Gauge Theory ◽  
Symmetry Breaking ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Gauge Theories ◽  
Square Lattice ◽  
Dirac Fermion ◽  
Topological Order ◽  
Continuous Transition

We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory that was recently shown in Monte Carlo simulations to exhibit Z2 topological order and massless Dirac fermion excitations. On tuning parameters, a confining phase with broken symmetry (an antiferromagnet in one choice of Hamiltonian) was also established, and the transition between these phases was found to be continuous, with coincident onset of symmetry breaking and confinement. While the confinement transition in pure gauge theories is well-understood in terms of condensing magnetic flux excitations, the same transition in the presence of gapless fermions is a challenging problem owing to the statistical interactions between fermions and the condensing flux excitations. The conventional scenario then proceeds via a two-step transition, involving a symmetry-breaking transition leading to gapped fermions followed by confinement. In contrast, here, using quantum Monte Carlo simulations, we provide further evidence for a direct, continuous transition and also find numerical evidence for an enlarged SO(5) symmetry rotating between antiferromagnetism and valence bond solid orders proximate to criticality. Guided by our numerical finding, we develop a field theory description of the direct transition involving an emergent nonabelian [SU(2)] gauge theory and a matrix Higgs field. We contrast our results with the conventional Gross–Neveu–Yukawa transition.

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 Tunable fractional quantum Hall phases in bilayer graphene

Science ◽  
2014 ◽  
Vol 345 (6192) ◽  
pp. 61-64 ◽  
Author(s):  
Patrick Maher ◽  
Lei Wang ◽  
Yuanda Gao ◽  
Carlos Forsythe ◽  
Takashi Taniguchi ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Electric Field ◽  
Degrees Of Freedom ◽  
Quantum Hall ◽  
Bilayer Graphene ◽  
Emergent Behavior ◽  
Topological Order ◽  
Fractional Quantum Hall ◽  
Model Platform ◽  
Quantizing Magnetic Field

Symmetry-breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field, electron interactions can cause spontaneous symmetry-breaking within the spin and valley degrees of freedom, resulting in quantum Hall effect (QHE) states with complex order. Here, we report fractional QHE states in BLG that show phase transitions that can be tuned by a transverse electric field. This result provides a model platform with which to study the role of symmetry-breaking in emergent states with topological order.

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.

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