Tag Info

Hot answers tagged

6

1) Gauge theory is a theory where we use more than one label to label the same quantum state. 2) Gauge “symmetry” is not a symmetry and can never be broken. This notion of gauge theory is quite unconventional, but true. When two different quantum states $|a\rangle$ and $|b\rangle$ (i.e. $\langle a|b\rangle=0$) have the same properties, we say that there ...


3

They are shown at the $\Gamma$ point in special diagrams called the reduced zone scheme in which a band will be shown folded back on itself. This way of showing the band structure is convenient for a few reasons, one of which is that it saves space on the page. If you look at that band gap at $\Gamma$ and follow the lower band down to lower energies, you ...


2

One can notice that: $$(n_{i\uparrow}-1/2)(n_{i\downarrow}-1/2) = n_{i\uparrow}n_{i\downarrow} -\frac{1}{2}(n_{i\uparrow}+n_{i\downarrow}) +\frac{1}{4} $$ To show the equivalence you can absorb the $(n_{i\uparrow}+n_{i\downarrow})$ term in the chemical potential. We don't care about the kinetic term, and have: $$ ...


2

TylerHG: Yes it is easy to calculate the density of states. But what I'm really asking here is "why." Note that a thin circular ring in $\mathbf{k}$-space of thickness $dk$ has area $dA=2\pi k\,dk$ (by elementary geometry). In $E$-space, since $E\propto k^2$, that ring corresponds to a patch of width $dE=2k\,dk$. Thus $$\frac{dA}{dE}=\pi.$$ But ...


2

It is easy to show that the total number of electrons in a 3D fermi sphere is : $$N(e)=\frac{V}{3\pi^2}*k_F^3$$ Where $k_F$ is the Fermi wave vector and $V$ is the real space volume of your sphere. Now if you rearrange for $k_F$ in terms of the total number of electrons you'll get a particular equation. It is know that ...


1

Indeed there is no relation between the sign of a potential and the sign of its Fourier transformation. But why should we care about this? In the field theory, the criterion is very simple, an interaction is attractive if its coefficient (in the Hamiltonian) is negative, and is repulsive if its coefficient is positive. According to this criterion, Altland ...


1

Let me answer your first question: Phase transition do not necessarily imply a symmetry breaking. This is clear in the example your are mentioning : The liquid-gas transition is characterized by a first order phase transition but there is no symmetry breaking. Indeed, liquid and gas share the same symmetry (translation and rotation invariance) and may be ...


1

I don't think that is the case. A useful reference is: http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.80.1083. One way to approach a theory of anyons is to start by writing down a list of particle types along with their fusion rules. Once doing this one may obtain consistency equations from solving the hexagon and pentagon equations arising from ...



Only top voted, non community-wiki answers of a minimum length are eligible