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Questions tagged [anyons]

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

The braid group is the group describing exchange of object in two-space dimensions, when knot between trajectories can happen.

One mainly distinguish between the Abelian and non-Abelian Anyons. The Abelian Anyons exchange is described by the uni-dimensional representation of the braiding group, whereas non-Abelian Anyons exchange is described by higher-dimensional representation(s) of the braiding group.

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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?
Timothy
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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 explain what physical properties of a system lead…
Mangler
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direct sum of anyons?

In the topological phase of a fractional quantum Hall fluid, the excitations of the ground state (quasiparticles) are anyons, at least conjecturally. There is then supposed to be a braided fusion category whose irreducible objects are in 1-1…
André
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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. Wikipedia), nor a (pseudo / fictitious) commutation…
FraSchelle
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How Non-abelian anyons arise in solid-state systems?

Recently it has been studied non-abelian anyons in some solid-state systems. These states are being studied for the creation and manipulation of qubits in quantum computing. But, how these non-abelian anyons can arise if all particles involved are…
Leandro Seixas
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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, here I submit another version of the question,…
Valter Moretti
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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, 035132, (2013)). But I have little knowledge about…
ZuoYou
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How are anyons possible?

If $|\psi\rangle$ 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 indistinguishable, the physical state cannot change…
Keshav Srinivasan
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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 sufficient I believe to understand this point, to be…
FraSchelle
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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: $$ Z=\exp\left[i\int\big( \frac{1}{4\pi} K_{IJ} a_I \wedge d a_J + a \wedge * j(\ell_m)+ a \wedge * j(\ell_n)\big)\right] $$ with…
wonderich
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Why is the phase picked up during identical particle exchange a topological invariant?

I've been wondering about the standard argument that the only possible identical particles in three dimensions are bosons or fermions. The argument goes like this: Consider exchanging the positions of two identical particles in 3D. Because the…
user94624
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Fermions, Bosons, Anyons on a 2-manifold

My understanding of fermions, bosons, and anyons is that anyons are disallowed in 3+1 dimensions (or $n+1 | n\geq3$) because of the topology of spacetime. The paths of swapping two particles twice is contractible in 3+1. In 2+1, this isn't the case…
orbita
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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 what about the braiding, fusion rules in …
Kai Li
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Resource recommendation for fractional statistics

A gentle yet comprehensive introduction to the concept of abelian and non-abelian statistics will be much appreciated.
Arnab Barman Ray
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Irrelevance of parastatistics for space dimension > 2

Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal (subspace where at least 2 particles have coincidental…
Squark
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