Questions tagged [anyons]
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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DMRG for anyons
I want to do some DMRG calculations for anyons. For example, consider the golden chain model for fibonacci anyons.
https://arxiv.org/pdf/cond-mat/0612341
I have two anyon types: $1, \tau$. However, ...
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Question about Path Integrals and Exchange Statistics in Steve Simon's "Topological Quantum"
In the introduction to the path integral approach leading to exchange statistics for many particles, Steve Simon breaks up the sum of paths into two types: paths where particles do not exchange (type ...
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Why the unit of quantum information for anyons systems should be the qubit?
I'm starting to learn more about anyons systems. I took a read on this article which is an introduction to topological quantum computing, and also took a look in other places like forums and some ...
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Chern-Simons (K matrix) theory and ${\rm Spin}^{\mathbb C}$ connections
If I understand correctly (e.g. from this paper), an Abelian bosonic Chern-Simons theory defined on $T^2\times \mathbb R$ is specified by a $K$ matrix via e.g. $S \sim \int_M K_{IJ}A^I \wedge dA^J$. ...
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Frobenius-Schur indicator and total orbital angular momentum
It is a well-known formula in the theory of anyons that $R_c^{ba}R_c^{ab}=\frac{\theta _c}{\theta _a\theta _b}$, where $R$ represents the braiding matrix and the $\theta$ are twists, i.e. the phase ...
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$F$-matrix rigidity condition in anyons
In Wang's "Topological Quantum Computation", the following condition of "rigidity" is imposed on the $F$-matrices characterizing basis changes of the topological Hilbert space for ...
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Anyons and Elementary particles in 2D [closed]
I'm doing my master's degree and I'm starting to learn more about Anyons. I want to understand more deeply why they can exist and how. I've done some research on the internet and found this question ...
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Qubits vs Fermions, Bosons and Anyons [closed]
I found out recently that qubits are different from fermions, bosons and anyons. And, which is why we use Jordan-Wigner Transformation to map them to their fermioinc counterpart. I think I am trying ...
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What physical properties give rise to abelian anyons as opposed to non-abelian anyons?
As far as I understand, abelian anyons are those which have a particle exchange operator which is a one-dimensional representation of the braid group. Non-abelian anyons, then, have a higher-...
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Since anyons cannot exist in our 3+1D world, what does it mean to have discovered them? Why should we study them?
There have been previous questions on this, for example see this and this question, but my question is different.
I get that in 2+1D, mathematically speaking, exchanging two identical particles twice ...
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Can Toric Code have a gapless boundary?
The toric code model is known to have two types of "gapped" boundaries, namely, the rough boundary and the smooth boundary. See, for example, Chap. 4.1 of this beautiful review https://arxiv....
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Fusion 2-categories for string-like excitations: a more concrete description?
I'm familiar with how fusion categories describe the fusion of point-like excitations, and how braided fusion categories describe the fusion of anyons in 2+1D topological order. Concretely, a fusion ...
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Does gravity exist in two spatial dimensions? [duplicate]
I've been studying anyons and was wondering if gravity exists in two spatial dimensions and how it affects these particles?
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Non-abelian Berry connection : clashing time-ordering conventions, and component-wise form
Let $\mathcal{M}$ be a $k$-dimensional parameter space associated to a quantum system with an $N$-dimensional ground state. As usual, we assume the system is subject to some adiabatic tuning of ...
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