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Dec
31
comment Edge states in the “half BHZ” model
Another claim I didn't make accurately is "the contributions [...] to the Chern number cancel, so due to bulk-edge correspondence there shouldn't be an edge state". The accurate version would be "the contributions to the Chern number cancel, so due to bulk-edge correspondence there should be the same number of left and right moving edge states on each edge". That is, a Hamiltonian with Chern number 0 can have edge states, but it's adiabatically connected to a Hamiltonian that doesn't. So the non-triviality of TIs is a global property, but by itself, the existence of edge states isn't.
Dec
31
comment Edge states in the “half BHZ” model
Well, yes, "edge state at $(0, \pi)$" wasn't accurate. What I meant was a state with $k_x=0, Re(k_y)=\pi$ and some small $Im(k_y)$ which determines the localization length (actually, the state is a linear combination of a state with small $Im(k_y)$ and a state with a large $Im(k_y)$ such that the vanishing boundary condition is satisfied). The existence of this state can be seen both by analytically solving the local Hamiltonian and by numerically diagonalizing the full Hamiltonian; doing the latter one sees that for M close to 4B the wavefunction changes sign between each y site. (continued)
Dec
30
comment Edge states in the “half BHZ” model
Is this extra formalism really necessary for the half BHZ model? The way I thought about it was, for M > 4B the contributions of $(0, 0)$ and $(0, \pi)$ to the Chern number cancel, so due to bulk-edge correspondence there shouldn't be an edge state at $k_x = 0$. Anyway, this doesn't quite answer the question since at it is at least partly possible to see changes in edge states from the local Hamiltonians. Expanding around $(0, 0)$ [$(0, \pi)$] one can see there's no localized solution for M < 0 [M > 4B] while there is one for M > 0 [M < 4B].
Dec
29
asked Edge states in the “half BHZ” model
Jun
7
comment Integrating out high momentum modes in $\phi^4$ theory
I've thought about it some more, and I'm no longer sure this is right. Shouldn't the $\lambda\hat{\phi}^4$ term have an affect on the low momentum modes due to intermediate states? For example, the following diagram represents a correction to the low momentum mass: img441.imageshack.us/img441/2263/blah1s.png (Single lines are low momentum, double lines are high momentum) Shouldn't there also be diagrams like img32.imageshack.us/img32/5949/blah12.png which further modify the low momentum mass and wouldn't exist if it weren't for the $\lambda\hat{\phi}^4$ term?
Jun
1
awarded  Supporter
Jun
1
asked Integrating out high momentum modes in $\phi^4$ theory
Mar
18
accepted Dirac magnetic monopoles and electric charge quantization
Mar
17
asked Dirac magnetic monopoles and electric charge quantization
Oct
5
awarded  Scholar
Oct
5
accepted Weak isospin confinement?
Oct
4
awarded  Student
Oct
3
asked Weak isospin confinement?