Stability of the bulk gap for quantum lattice systems

I will discuss recent work proving that uniformly small short-range perturbations do not

close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a

standard local topological quantum order condition. In contrast with earlier results, we do not

require a positive lower bound for finite-system spectral gaps uniform in the system size. To obtain

this result, we extend the Bravyi-Hastings-Michalakis strategy so it can be applied to perturbations

of the GNS Hamiltonian of the infinite-system ground state.