= Particle-hole symmetry of a half-filled bipartite band
{title2=$\mu(T)=\epsilon_0$}
A nearest-neighbour <tight-binding model> on a bipartite lattice, with identical on-site <energy> $\epsilon_0$, has paired single-particle <energies> $\epsilon_0\pm x$. At half filling, $f(\epsilon_0+x)+f(\epsilon_0-x)=1$ for the <Fermi-Dirac distribution> with $\mu=\epsilon_0$. Thus its fixed-density <chemical potential> equals $\epsilon_0$ at all positive <temperatures> within the isolated-band model. An anisotropic rectangular nearest-neighbour band retains this property; additional same-sublattice hopping or unequal on-site <energies> can remove it.
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