Stability of Gapped Ground States

Mathphys Seminar

I will review several recent results about the ground state gap of quantum many-body systems and the question of spectral gap stability under perturbations. I will discuss results for the AKLT model on the hexagonal lattice, in particular the Local Quantum Topological Order (LTQO) property for it. The LTQO property will be further clarified by considering two one-dimensional models with multiple ground states: certain Haldane pseudopotentials and the Temperley-Lieb spin chains. For the first I will present a new gap stability result. The latter provide examples of an unstable ground state gap.