A short proof of stability of topological order under local perturbations

摘要: Recently, the stability of certain topological phases matter under weak perturbations was proven. Here, we present a short, alternate proof same result. We consider models quantum order for which unperturbed Hamiltonian $H_0$ can be written as sum local pairwise commuting projectors on $D$-dimensional lattice. perturbed $H=H_0+V$ involving generic perturbation $V$ that short-range bounded-norm interactions. prove if strength is below constant threshold value then $H$ has well-defined spectral bands originating from low-lying eigenvalues $H_0$. These are separated rest spectrum and each other by gap. The width band smallest eigenvalue decays faster than any power lattice size.