New answers tagged lattice-model
A proof of the Nielsen-Ninomiya theorm, basically based on your quite ingenious suggestion is given in section 7 of Elias Kiritsis article on the topological properties of the Berry's phase.
Since you have a Hamiltonian with discrete sites, I assume that you consider a periodic lattice. For a periodic one-dimensional chain with unit lattice constant, all independent solutions, labelled by $k$, can be chosen to lie in the first Brillouin zone $k \in [-\pi,\pi]$ of the 1D $k$-space. This is because the only values of the wave function that matter ...
When there is only one type of atom, we only need one equation of motion. When there are two types of atoms, we need two equations, one for each type. For example, a FCC lattice with the corners occupied by one type of atom, and the face centers occupied by another type requires two equations. The number of neighbors does not increase the number of ...
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