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Questions tagged [skyrmion]

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Why are the expressions of the Skyrme Model related with a kinetic and a mass term?

I was reading about the Syrme Model Lagrangian, $$ \mathcal{L} =-f^2_\pi/4 Tr(L_\mu L^\mu) + 1/32e^2 Tr([L_\mu,L_\nu]^2)- \frac{\mu^2}{2} Tr(1-U) $$ where $L_\mu=U^\dagger \partial_\mu U$. I've read ...
Gorga's user avatar
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Concise formula for Skyrmion number of a four-band Hamiltonian

The Haldane model on the honeycomb lattice is often written as $H=\sum_{i=0}^3 \vec{d}_i\cdot \vec{\sigma}_i$ where $\vec{\sigma}$ is the vector of Pauli matrices and $\vec{d}$ is a vector of ...
Joshuah Heath's user avatar
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Hopfion with only in-plane vortex rather than skyrmion along the torus?

A simple torus-like hopfion with hopf charge $Q_H=1$ will typically exhibit a skyrmion at each slice cutting the toroidal circle. What if the skyrmion is replaced by an in-plane 2D vortex, i.e., we ...
xiaohuamao's user avatar
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What is the modern status on the Skyrmion theory of baryons?

It was noticed in the 1960s that chiral perturbation theory, describing the goldstone-bosons (pions) of the breaking $SU(N_f)_L \times SU(N_f)_R \to SU(N_f)_V$ of the chiral symmetry, has solitonic ...
QCD_IS_GOOD's user avatar
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1 answer
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Circular symmetry argument in integration

I'm working through a book on magnetic skyrmions and in some calculations the integral $\int d^2 \vec{r}\, \left(\partial_x \vec{S}\right)\cdot\left(\partial_y \vec{S}\right)$ pops up, where we ...
Math Math's user avatar
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What is the difference between a skyrmion and a magnetic vortex?

Skyrmions and magnetic vortices are spin structures occurring in magnets. What are the differences between them? More specifically, I would like to understand their origin and how to distinguish them.
B. Brekke's user avatar
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A primer on topological solitons in scalar field theories

As the title suggests I want to learn more about topological solitons in scalar field theories. I am searching for a resource which is self-contained, in the sense that it also explains the ...
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1 answer
236 views

How does the Mermin-Ho theorem handle singularities arising from the hairy ball theorem?

I am reading about the derivation of the Mermin-Ho relation in chapter III. B of (Kamien, 2002) and trying to understand how it fits with the hairy ball theorem. Assuming you have a unit vector $\hat{...
Ben's user avatar
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What is physical significance of $k$-space topology?

I am working with topological materials and I do understand what topology is. While reading papers, I am not able to understand the "nontrivial k-space topology". How skyrmions are mostly ...
ashice's user avatar
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How "hedgehog" or instanton event changes the configuration of neel vector in 2D antiferromagnet?

The definition of "hedgehog" or instanton event here is "a space-time event where the skyrmion number Q changes by $\pm1$ is called a hedgehog" (ref.1 & 2). A nice figure ...
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Skyrmion number

The skyrmion number is defined as $$n=\frac{1}{4\pi}\int\mathbf{M}\cdot\left(\frac{\partial\mathbf{M}}{\partial x}\times\frac{\partial\mathbf{M}}{\partial y}\right)dxdy$$ where $n$ is the topological ...
Eric Z's user avatar
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What are Skyrmion bubbles?

what exactly is the difference between a skyrmion and a skyrmion bubble? Thanks.
IrDa's user avatar
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How to derive the Einstein-Skyrme equations?

I would like to derive the Einstein-Skyrme equations. The action can be read as \begin{equation} S[g,U] = \int d^{4}x\sqrt{-g}\biggl[R + \frac{K}{4}Tr\bigg(A^{\mu}A_{\mu} + \frac{\lambda}{8}F_{\mu\...
Hello's user avatar
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2 votes
1 answer
530 views

What does topologically stable mean?

I am working on an article about skyrmion manipulation and it is written that those particles are "topologically stable particle-like spin configurations that carry a characteristic topological charge ...
Epaline's user avatar
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2 votes
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No global monopoles in QCD

If a global symmetry gets both spontaneously and explicitly broken, the explicit symmetry breaking pattern is crucial for understanding the formation of topological defects. For example, in the axion ...
Thomas's user avatar
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Number of baryons in the Skyrme model

In QCD, the Eightfold Way organizes the number of baryons with respect to their flavor and color quantum numbers: for three light $(u,d,s)$ quark constituents, a spin-(1/2) baryon octet and a spin-(3/...
Thomas's user avatar
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2 votes
1 answer
121 views

Skyrmion of pseudo-scalar mesons and vector mesons

I had heard statements that Skyrmion of pions (pseudo-scalar mesons) cannot be an object like baryon, however, Skyrmion of vectors mesons may indeed form an object like baryon. For example, see this ...
wonderich's user avatar
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7 votes
2 answers
1k views

Non-chiral skyrmion v.s. Left/Right chiral skyrmion

A skyrmion in a 3-dimensional space (or a 3-dimensional spacetime) is detected by a topological index $$n= {\tfrac{1}{4\pi}}\int\mathbf{M}\cdot\left(\frac{\partial \mathbf{M}}{\partial x}\times\frac{...
wonderich's user avatar
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4 votes
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half Skyrmion vs Meron

Is there a difference between a half skyrmion and a meron? I'm asking this in regard to half skyrmion theories of High Tc Superconductors. It would be interresting to know if the proposed half ...
P3trus's user avatar
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