Anyons is the generic name for the particles which interchange among other according to the representation(s) of the braid group.

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How is a half twist of a diagram equivalent to exchanging anyons?

Consider the fusion of $a$ and $b$ to form $c$, with the exchange of anyons $a$ and $b$, as per Pachos' book Introduction to Topological Quantum Computation. I'm confused how the half twist of $c$ ...
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Identical particles and topological phases

I've been wondering about the argument that is always put forward for why the only possible identical particles in three dimensions or more are bosons or fermions. My question is related to a very ...
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Different anyon condensations that share the same phase

In Kitaev's notes, he reviewed the toric code model. Consider on square lattice the Hamiltonian $H=-J_e \sum_s A_s-J_m \sum_p B_p,\ A_s=\prod_{j\in vertices} \sigma_j^x,\ B_p=\prod_{j\in plaquettes} ...
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What are the instances of usage of four color theorem in the theory of fractional statistics?

How important is four-color theorem (Hypothesis) in theory of Fractional Statistics?
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Which quasiparticles follow which statistics [closed]

Let me say beforehand that I know this is an ill-defined question, but I believe it is useful anyway. For these common quasiparticles: Phonons Holes Plasmons Excitons Plasmon-polaritons What ...
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Wen plaquette model with one kind of plaquette operator

Let us say that we modify the familiar Wen plaquette model so that only one kind of plaquette operator is in the Hamiltonian which is a product of $\sigma_z$s, what kind of topological order or state ...
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Mean field approach to toric code

Toric code is one of the few exactly solvable model in condensed matter, however, like the paper (http://arxiv.org/abs/1104.5485) that uses SU(2) slave fermion to "solve" Kitaev's honeycomb model, is ...
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What determines the anyon fusion outcome (if several are possible)?

Given the fusion rule (for anyons) "A x B = 1 + C" it is possible for the anyons A and B to fuse to the vacuum "1" or to fuse to the anyon C. What determines what will happen if they fuse? Is the ...
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Relationship between modular transformations and anyon braiding

In the context of anyon braiding, we have $S$ and $T$ matrices which describe the mutual and self statistics of anyons. In the context of conformal field theory on a torus, we have modular ...
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81 views

properties of p-wave superconductors in a self consistent calculation

2D p+ip superconductors have zero energy mid-gap modes localized at the boundaries as well as in the vortex cores as pointed out in several places such as Read, Green and Ivanov. The modes result in ...
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91 views

Diagonal part of the configuration space of two indistinguishable quantum particles

Why is the configuration space of two indistinguishable particles given by $\frac{M^n-\Delta}{S_n}$? My question is about the $\Delta$. (Notation: $M$ is the configuration space of 1 particle. $M^n$ ...
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How to read the indicies of the Fusion Matrix F for Anyons

I am reading "Introduction to Topological Quantum Computation" from J. K. Pachos (first script from his Website: http://quince.leeds.ac.uk/~phyjkp/Files/IntroTQC.pdf). I can't seem to understand ...
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Limitations of Quantum Simulations on a Classical Computer

My question is on the simulation of a quantum computer on a classical machine. I understand that a classical computer to simulate any quantum algorithm--the problem is that the quantum computer does ...
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Anyonic Braiding and Conformal Field Theory

I am looking for resources (both pedagogical and newer research articles) on the connection between topological quantum computation and conformal field theory. In particular, a CFT description of ...
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Braiding in 3D Space

In arXiv:1005.0583 the authors wrote that in two dimensional space the configuration space of n particles is multiply-connected and therefore the fundamental group of the configuration space is the ...
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Rigorous definition of superselection sector/quasiparticle type in anyon systems

The systems I have in mind are for example Kitaev's toric code model (arXiv:quant-ph/9707021) and Kitaev's honeycomb model (arXiv:cond-mat/0506438). What I'm looking for is a mathematically rigorous ...
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186 views

Topological Quantum Computing beyond Anyonic Braiding

In materials such as those that exhibit fractional quantum hall states, the ground-state topological degeneracy is known to be robust against external perturbations. This ultimately tells us that we ...
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176 views

What does it mean physically if pentagon identity or hexagon identity doesn't have any answers?

Imagine I write a fusion rule for some anyons on a paper. Then, I try to solve Pentagon identity and Hexagon identity, imagine finally I find out for example the Hexagonal equation doesn't have any ...
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Toric Code and the String-Net Model

What, exactly, makes the toric code a quantum error-correcting code as opposed to any other string-net model? What makes it special? The way I understand it, it's a normal string-net model on a torus, ...
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107 views

Dilemma: Fusion space from a direct sum of anyons or NOT

In Preskill's note, 9.1.2 in page 44, concerning the fusion space, it states that: The fusion rules of the model specify the possible values of the total charge $c$ when the constituents have ...
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Anyonic braiding statistics from density matrix renormalization group (DMRG) simulations

How does the ground state energy of the system change when we braid two anyons? Can the braiding of anyons be simulated with a computational method such as the density matrix renormalization group, ...
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1answer
158 views

How the Vortex containing majorana bound state is non-abelian statistics

Recently,I read some papers about non-abelian statistics of majorana fermion, such as: Majorana Returns F. Wilczek http://www.nature.com/nphys/journal/v5/n9/full/nphys1380.html and Non-Abelian ...
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Axiom approach for majorana fermions

This is the usual way of introducing majorana operators. First we have $N$ fermionic modes. The corresponding operators satisfy the commutation relations $$ \{c_i, c_j \}= \{c_i^\dagger, c_j^\dagger ...
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Does fractional charge imply fractional statistics?

Does fractional charge imply fractional statistics (e.g. anyons)? If not, are there some relations between them?
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285 views

Anyons: Effect of braiding on fusion multiplicities

In the theory of non-abelian anyons, essential information is stored in the fusion multiplicities or Verlinde coefficients $N_{ab}^c$. Having the Pants Decomposition in mind, it is possible to use ...
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Angular momentum of anyons

Why is it true that anyons can have angular momentum taking any real value? Why aren't they restricted to the $j(j+1)$ integer values most are familar with?
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Has the existence of anyons been experimentally verified?

I've been wondering whether there has been any experimental evidence for the existence of anyons or are they just objects of purely mathematical interest?
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Anyons only in 2+1 spacetime dimensions - better explanation

Regrading why anyons exist only in 2+1 spacetime dimensions (which have an arbitrary phase on exchange), I read the reason that the paths for exchange in 3D are deformable into each other while in ...
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221 views

Is there a wave function for anyons?

People talk about anyons a lot. But i have never seen an anyon wave function. I suspect that there is no such thing as a wave function for anyons. I mean, anyons are not generalizations of bosons ...
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Qubit in Type 1.5 superconductor?

I'm interested in Type 1.5 superconductors, first proposed by Egor Babaev in 2002 and found in the laboratory in 2009 (magnesium dibromide). Such conductors favor small bundles of vortices. The most ...
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How are anyons possible? (another version)

I know that this question has been submitted several times (especially see How are anyons possible?), even as a byproduct of other questions, since I did not find any completely satisfactory answers, ...
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381 views

Experimental evidence for non-abelian anyons?

Since non-abelian anyons have become quite fashionable from the point of view of theory. I would like to know, whether there has actually been experimental confirmation of such objects. If you could ...
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an Abelian complex statistical phase from exchanging non-Abelian anyons?

We have some discussions in Phys.SE. about the braiding statistics of anyons from a Non-Abelian Chern-Simon theory, or non-Abelian anyons in general. May I ask: under what (physical or mathematical) ...
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Braiding statistics of anyons from a Non-Abelian Chern-Simon theory

Given a 2+1D Abelian K matrix Chern-Simon theory (with multiplet of internal gauge field $a_I$) partition function: $$ Z=\exp\left[i\int\big( \frac{1}{4\pi} K_{IJ} a_I \wedge d a_J + a \wedge * ...
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Questions on the elementary excitations in the resonating-valence-bond(RVB) states?

It is known that the RVB states can support spin-charge separations and its elementary excitations are spinons and holons. But it seems that there are some different possibilities for the nature of ...
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How are anyons possible?

If $|ψ\rangle$ is the state of a system of two indistinguishable particles, then we have an exchange operator $P$ which switches the states of the two particles. Since the two particles are ...
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152 views

Non-abelian behavior of vortices in p-wave superconductors

I am trying to understand why vortices in p-wave superconductors are actually non-abelian anyons and how this relates to Majorana modes. However I am having a hard time finding proper resources (in ...
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What is parafermion in condensed matter physics?

Recently, parafermion becomes hot in condensed matter physics (1:Nature Communications, 4, 1348 (2013),[2]:Phys. Rev. X, 2, 041002 (2012), [3]:Phys. Rev. B, 86, 195126 (2012),[4]:Phys. Rev. B,87, ...
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Is the symmetrisation postulate unnecessary according to Landau Lifshitz?

The symmetrisation postulate is known for stating that, in nature, particles have either completely symmetric or completely antisymmetric wave functions. According to these postulate, these states are ...
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Topological quantum computation : Anyon model

Could someone tell me about Frobenius-Schur indicator and the associated cups and caps notation in context of anyon model. One possible reference could be Parsa Bonderson thesis which is freely ...
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195 views

Topological quantum computation: abelian vs. non-abelian anyons

We need non-abelian fractional hall states because of the ground state degeneracy http://rmp.aps.org/abstract/RMP/v80/i3/p1083_1 (arXiv version for free). But we can also have degeneracy even in case ...
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Can anyons emerge from momentum-space other than spatial dimensions?

So far in condensed matter physics, I only know anyons(abelian or nonabelian) can emerge as quasiparticles in 2D real-space. But is there any possibility to construct anyons in momentum-space ? And ...
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333 views

Anyons without fractional spin?

Is it possible to have particles obeying anyonic statistics but not having fractional spin? I am wondering, because while spin in quantum physics arises from the geometry/topology of spacetime, ...
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567 views

What is the reason why anyons escape spin-statistic theorem?

I'm wondering about the exact reason why anyons escape the spin-statistic theorem (SST), see e.g. http://en.wikipedia.org/wiki/Spin–statistics_theorem. I've read somewhere (the wikipedia page is ...
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Anyons as particles?

I'm trying to understand the basics of anyons physics. I understand there is neither a Fock space they live in (because Fock is just the space of (anti-)symmetrized tensor product state, see e.g. ...
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527 views

Some questions about anyons?

(1) As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" ...
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Basic questions in Majorana fermions

Why any fermion can be written as a combination of two Majorana fermions? Is there any physical meaning in it? Why Majorana fermion can be used for topological quantum computation?
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Topological Charge. What is it Physically?

I have seen the term topological charge defined in an abstract mathematical way as a essentially a labeling scheme for particles which follows certain rules. However I am left guessing when trying to ...
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Modeling non-quantum objects (in finance, sociology etc) using fermionic fields?

Please provide (if any) applications of fermionic field theory in non-physics macro contexts (finance, sociology etc). I see only bosonic fields being used mostly. The only (minor) application of ...
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Anyonic phase factors when encircling one about another

The question Statistics of bound states of anyons with order pq, and its answer inspires this question. Suppose you have an anyonic particle with nonintegral spin s. Presumably, if there's an ...