# Tag Info

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"Total spin conservation" means global $SU(2)$ spin-rotation symmetry (a continuous symmetry) of the Heisenberg model, and "spin wave" indicates an ordered ground state that spontaneously breaks the spin-rotation symmetry. Thus, according to Goldstone theorem, there must be a gapless mode for spin wave.

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Topological degeneracy is only defined in the thermodynamic limit on a closed manifold. The ground state degeneracy of a finite-sized system or on an open manifold is not "topological", and can not be called topological degeneracy. Considering your examples. (1) The ground state degeneracy is ill-defined with open boundary condition. Because there might be ...

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Yes, there is a structural reason for the existence of flat band on the Kagome lattice. This is related to the wave function localization due to the destructive interference on the lattice. The flat band has many physical interpretations. In the momentum space, looking at the dispersion relation, a flat band means the effective mass of the particle is ...

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With solids atoms are mostly locked in place so it makes sense there can be lots of different crystal structures and atomic packings. For liquids and gases though their defining characteristic is that their atoms are mobile enough to flow and fill a container. You can't both have structure and mobility.

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Again, thanks to the $SU(2)$ PSG proposed by prof.Wen, I can answer my question now, $THT^{-1}$ is in fact $SU(2)$ gauge equivalent to $H$, and the statement "$H$ is also not SU(2) gauge equivalent to the time-reversal transformed Hamiltonian $THT^{-1}$" in my question is wrong. Let's rewrite the Hamiltonian as ...

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I don't know the article you refer to, but I believe the Hamiltonian you discuss should get a $\pi$-phase shift after one turn around a (2D) lattice cell. So I guess it should read $H=F^{\dagger}\cdot H_{\pi}\cdot F$ with H_{\pi}=t\left(\begin{array}{cccc} 0 & e^{\mathbf{i}\pi/4} & 0 & e^{-\mathbf{i}\pi/4}\\ e^{-\mathbf{i}\pi/4} & 0 & ...

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1. Are there two definitions of TIs, one for usual TIs, and another (wider) including HgX? No, there is only one definition a 3D band topological insulator (TI): the $\mathbb{Z}_{2}$ classification scheme proposed by Fu, Kane, and Mele: Liang Fu, Charles L. Kane, and Eugene J. Mele. “Topological insulators in three dimensions.” Physical Review ...

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In general, both IQHE and FQHE are rigid quantum states, whose rigidness is protected by the finite energy gap ($h\omega$ for IQHE) between the ground state(s) and the exited states. Finite temperature can support excitations to overcome the gap, which destroys the rigidness of the state. Under finite temperature, the quantization of the Hall conductivity is ...

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In the graph, Electron energy is the independent variable Density of states is the dependent variable i.e., "density of states is a function of electron energy". For 99% of graphs that you've ever seen in your life, the independent variables is plotted on the x-axis and the dependent variable on the y-axis. But for this graph, it's the opposite! Here, ...

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The material may become opaque for radiation that has frequency close to resonance frequencies of the material. The electrons in matter are sensitive to radiation in certain ranges of frequencies (absorption peaks or bands) and can get excited. This is accompanied by stronger absorption of the radiation. The electrons are sensitive to certain resonance ...

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The short answer is yes. One can convince oneself this is indeed the case by doing the dimensional counting as it was done by Everett You. However, it is by no means a proof. The problem is that the valence bond states are not linearly independent. Even though there are much more valence bond states than the number of singlets made from $N$ spin-one-half ...

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The short answer is, yes, the chiral edge state is determined by bulk topological property. It is known as bulk-edge correspondence. The paper you should read is: Protected edge modes without symmetry - 1301.7355. Generically, to determine whether the edge states are robust is by determining whether the edge states are protected'' by any of the three ...

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Simple, combine both real- and $\mathbf{k}$-space pictures! The basic idea is to split up your $n$-dimensional system into multiple $(n-1)$-dimensional systems. For example, say you have a 2D square lattice and you define your edges along the $x$-direction. Then you need to break the 2D lattice into 1D lattices pointing in the $x$-direction. In other words, ...

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They don't relate. The primitive unitcell is a property of the lattice. The lattice has nothing to do with the basis. You can have a single atomic basis or a thousand atomic basis but both have the same lattice, and therefore the same primitive unit cell. One of the most important facts you have to wrap your head around is that a lattice point has nothing ...

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First of all, the Pauli matrices are not space-time dependent, so of course you can pass the derivative right through them. Second of all, $\operatorname{Tr} [\partial(\vec{\pi}\cdot\vec{\tau})]^2 = \operatorname{Tr}\partial_\mu \pi^i \partial^\mu \pi^j \tau^i \tau^j$ Now remember $\tau^i \tau^j = i \epsilon_{ijk} \tau^k + \delta^{ij} I_{2x2}$ So ...

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