# Tag Info

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I'll state one version of the theorem, valid for classical systems. I'll not give the most general framework, as things become messy, but this should still give you an idea of how general the result is. We need the following ingredients: Spins: to each vertex of the lattice $\mathbb{Z}^2$, we attach a spin $\phi_x$ taking values in some compact ...

7

The slave particle approach is based on the assumption of spin-charge separation in the strongly correlated electron systems (typically Mott insulators). It was proposed that the electrons can decay into spinons and chargons (holons/doublons). But to preserve the fermion statistics of the electrons, the spinon-chargon bound state must be fermionic, so the ...

4

When talking about crystal lattices, the lattice vectors are what determines the translational symmetry of the crystal, and you have correctly identified those. The basis vectors are the vectors that tell you where the different atoms in your unit cell are. Thus, the basis vectors are those "locations of atoms A and B": The basis vector for atom B is just ...

3

A current is nothing than charged particles moving. Since those charged particles also have a mass, it follows that they cannot possibly reach the speed of light. In a real material that conducts electricity, the average net velocity of charges is actually very, very low, because they bump into atoms all the time, which basically sends them flying off in ...

3

I am going to try and reinterpret some of that paper, see if we can get some kind of answer started. Please comment and contribute, I think this is an interesting physical system. It would seem that they are using the fact that there are both boson (symmetric) and fermion (antisymmetric) representations of $SU(N)$ to generalize the usual $SU(2)$ magnet. The ...

3

There are many schemes to make topological superconductors. Some of these schemes have restrictions on the chemical potential $\mu$. You also need to know what type of topological superconductors you are dealing with. You can refer to the periodic table to determine this: In the paper from the link you provided the authors mention two types of ...

3

Short answer: No. As you pump more and more air into the container, the pressure rises and rises. At some point, the molecules are so close to each other that instead of a gas, you get a liquid. If you continue even more, eventually you'll get a solid. In this solid, atoms/molecules are arranged in a regular pattern with well defined distances between ...

3

This is quite a standard textbook example. Good treatments can, for example, be found in Altland (Condensed Matter Field Theory) or Nagaosa (Quantum Field Theory in Condensed Matter Physics). However, the basic reasoning can be understood quite easily: Consider the change in angle produced as we perform a closed loop around some point. Naively we obtain ...

3

Technology has evolved a bit compared to what was described by Martin Beckett. Many powder diffractometers still use the setup he describes, but mirrors are becoming more and more common at laboratory powder diffractometer sources. However, these mirrors do not aim to focus the beam, they collimate the beam (try to make sure that as much as possible of the ...

2

The states at $\Phi$ and $\Phi + \Phi_0$ are related by a gauge transformation[1] and therefore the spectrum must be the same. For concreteness let's talk about electrons fixed to a ring of radius $R$. Parameterize the wavefunction $\psi$ by the arclength $l$. Periodicity requires that $$\psi(l +2\pi r) = \psi(l).$$ There is some hamiltonian $H$ on the ring ...

2

Well, the answer is yes and no. The band inversion between the $s$-like (conduction) band $\Gamma_6$ and $p$-like (valence) band $\Gamma_8$ in HgTe is primarily responsible for its topologically nontrivial band structure. The bulk band structure of HgTe with (right) and without (left) spin-orbit coupling is shown in the figure below. There are a total of ...

2

I was wondering about exactly the same question some days ago, reading the seminal paper of Mermin (Rev. Mod. Phys. 51, 591--648 (1979), The topological theory of defects in ordered media), where you find an introductory discussion for the example of spins within the two-dimensional plane. There you find a lot of plots with spins (depicted as arrows in the ...

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The toy example is localization on the Bethe lattice (AKA the regular Cayley tree). There is a paper by Abou-Chacra, Thouless and Anderson that discusses this. Or you can just google around. R. Abou-Chacra et al 1973 J. Phys. C: Solid State Phys. 6 1734 or R. Abou-Chacra and D.J. Thouless, J. Phys. C 7 (1974), 65.

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Why do you want to have an understanding of the gapless edge states without using bulk topology? If you allow me to use the bulk topology, an argument is that you can continuously move the edge and consider that as an adiabatic parameter which interpolate two systems. To be more precise, you can consider a sphere with part of it in one topological state A ...

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There could be more to it. I have learned a quite different meaning of "basis" when it comes to crystallography: Of course, lattice vectors are the vectors that span the lattice. Now, at each lattice site, the crystal can have one or more "basis atoms". That's when we speak of a one-atomic, two-atomic basis etc... The positions of the basis atoms are ...

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Hand-wavingly, I would say that boundary conditions are important here. If you confine charges with anything, I am not sure your charges will interact exactly in 2D. However, if the field lines cannot escape in the direction perpendicular to the trapping plates, you "force" them to exist in 2d so to speak. Most likely the slab is neutral in width but charge ...

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In ferromagnetic materials there is an unpaired electron in the outermost orbital, giving an overall magnetic moment equal to one electron spin to the atom. In a ferromagnetic bulk crystal, these orbitals can overlap between neighbouring atoms which causes the spontaneous magnetisation through the exchange interaction. This interaction is incredibly short ...

2

As I recall (it was thirty years ago!) the main interaction is between neutrons and atomic nuclei, which is presumably a strong force interaction. The neutrons have no significant direct coupling to electrons, but the nuclei are charged so displacing a nucleus interacts with the electrons and can transfer energy to them. Neutrons have a non-zero magnetic ...

2

There is no contradiction between the explanation of the tricritical point in the Wikipedia article and the usage of the term in the paper. In the latter, they use a model which consists of several components and exhibits phase transitions. They identify a tricritical point which fits the definition in the Wikipedia article.

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The corollary can be inferred from the Goldstone theorem: If the ground state breaks a continuous symmetry, there are gapless excitations. Thus, if the system is gapped, the symmetry cannot be spontaneously broken in the ground state. This does, of course, not explain how the corollary follows from the Mermin-Wagner theorem (and it holds in any spatial ...

1

Okay, my comments are getting too much, so I will answer. If I understand your question correctly it says this: Papers show that the non-planar Ising model (finding its ground state) is NP complete On the other hand, finding the eigenvalues of a matrix is polynomial. So how do these points reconcile? The important point here is in the size of the input. ...

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Two scenarios let this happen in 3D space: The field is confined to die out in one direction with e.g. conducting slabs. The field can then be separated into xy and z components, i.e. f(x,y)g(z) for the right bump function g. If you're dealing with appropriately confined electrons, the z-component of the potential doesn't have any effect on dynamics and ...

1

It's because the electrons in the conduction band are correlated, motion and spin are not uncorrelated since pauli principle is acting, if the spins are opposite the motion can be more "free", but if they point towards the same direction they can be closer (conterintuitevely) Exchange interaction

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In a way, the reciprocal lattice is the Fourier transform of the original lattice. Now it's in the nature of the Fourier transform to change a sub- into a superstructure. That means that the basis vectors (i.e. the sub-structure of your unit cell) in real space lead to a super-structure in reciprocal space. So, the reciprocal lattice vectors define a ...

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Symmetric case I'll first explain the definition of the surface tension between two ordered phases of the Potts model, since the symmetry between the phases simplifies things. I'll work in dimension $3$ to be specific, but everything generalizes in a straightforward way to other dimensions. So consider the $q$-states Potts model at inverse temperature ...

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Basis vectors and lattice vectors are alternative ways to represent vectors in a vector space. In mathematics (linear algebra,) basis vectors are mutually orthogonal and form a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space. A set of basis vectors define what we usually think of as a ...

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To my knowledge, a general formula does not exist. The modification of the band gap heavily depends on the doped material and the dopant. For moderate dopings, there seems to be an answer on this link I found with a quick google search : http://ecee.colorado.edu/~bart/book/book/chapter2/ch2_3.htm Look at section 2.3.3.4. This might fall into what you are ...

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There are a number of related ways of thinking about this. The answer of webb can be put on a slightly more explicit ground. In the "spin coherent states" path integral for the quantum Heisenberg model, solutions of the classical Heisenberg model are extrema (or saddle-points). You could also, more prosaically, perform a Holstein-Primakoff transformation to ...

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For the vacuum/HgTe you'd have 2D TI somewhere on surface of HgTe which is not very convenient for study of this state. In addition, surface defects will make the result hardly usable even for experiments, don't even think of applications. In CdTe/HgTe/CdTe QW you have a good control on the properties of the system, it has a perfect lattice, etc.

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Let us treat the "coherent" part first. Neutrons scatter off nuclei, and the strength of the scattering thus depends not only on atomic number, but also which isotope we are dealing with. If one of the elements in our sample has two or more common isotopes, these isotopes will be randomly distributed throughout the crystal, since the chemistry of different ...

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