Topological order with a twist: Ising anyons from an Abelian model.

@article{Bombin2010TopologicalOW,
  title={Topological order with a twist: Ising anyons from an Abelian model.},
  author={H. Bombin},
  journal={Physical review letters},
  year={2010},
  volume={105 3},
  pages={
          030403
        }
}
  • H. Bombin
  • Published 2010
  • Physics, Medicine
  • Physical review letters
Anyon models can be symmetric under some permutations of their topological charges. One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry. We study the realization of such defects in the toric code model, showing that a process where defects are braided and fused has the same outcome as if they were Ising anyons. These ideas can also be applied in the context of topological codes. 
Non-Abelian statistics with mixed-boundary punctures on the toric code
The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibitExpand
Structure of 2D Topological Stabilizer Codes
TLDR
It is proved that two non-chiral codes are equivalent under local transformations iff they have isomorphic topological charges. Expand
Symmetry fractionalization and twist defects
Topological order in two dimensions can be described in terms of deconfined quasiparticle excitations - anyons - and their braiding statistics. However, it has recently been realized that this dataExpand
Local realizations of anyon exchange symmetries without lattice dislocations
The global e-m exchange symmetry of the toric code is realized locally through an exactly solvable Hamiltonian on a two dimensional lattice which has no lattice dislocations and their associatedExpand
Globally symmetric topological phase: from anyonic symmetry to twist defect.
  • J. C. Teo
  • Physics, Medicine
  • Journal of physics. Condensed matter : an Institute of Physics journal
  • 2016
TLDR
In this article, the most recent theoretical developments on symmetries and defects in topological phases are reviewed. Expand
Theory of Twist Liquids: Gauging an Anyonic Symmetry
Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topologicalExpand
The Quantum Double Model with Boundary: Condensations and Symmetries
Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterizeExpand
Universal topological phase of 2D stabilizer codes
Two topological phases are equivalent if they are connected by a local unitary transformation. In this sense, classifying topological phases amounts to classifying long-range entanglement patterns.Expand
Fractal symmetries: Ungauging the cubic code
Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of theExpand
A topological phase transition on the edge of the 2d Z2 topological order
The unified mathematical theory of gapped and gapless edges of 2d topological orders was developed by two of the authors. It provides a powerful tool to study pure edge topological phase transitionsExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 55 REFERENCES
Fractional statistics and anyon superconductivity
The occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, theExpand
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)Expand
Ann
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixedExpand
and M
  • Terhal, arXiv:1004.3791
  • 2010
Physical Review Letters 63
  • 1989
Found
  • C. Ross
  • Medicine
  • The Dental register
  • 1869
Phys
  • Rev. Lett. 103, 090501
  • 2009
Physical Review B
Phys
  • Rev. A 81, 032301
  • 2010
...
1
2
3
4
5
...