Sergey Bravyi, David Gosset, et al.
QIP 2020
Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed Hamiltonian H0 can be written as a sum of local pairwise commuting projectors on a D-dimensional lattice. We consider a perturbed Hamiltonian H = H0 + V involving a generic perturbation V that can be written as a sum of short-range bounded-norm interactions. We prove that if the strength of V is below a constant threshold value then H has well-defined spectral bands originating from the low-lying eigenvalues of H0. These bands are separated from the rest of the spectrum and from each other by a constant gap. The width of the band originating from the smallest eigenvalue of H0 decays faster than any power of the lattice size. © 2011 Springer-Verlag.
Sergey Bravyi, David Gosset, et al.
QIP 2020
Sergey Bravyi, David Gosset
Physical Review Letters
Sergey Bravyi, David Fattal, et al.
Journal of Mathematical Physics
Sergey Bravyi, Matthew B. Hastings
STOC 2014