Realizability of split states as gapped ground states

Determine whether every split state on a one-dimensional quantum spin chain is the gapped ground state of some local Hamiltonian.

Background

Split states arise naturally in the analysis of low-entanglement infinite-volume states and include all one-dimensional gapped ground states by Matsui’s theorem. The classification program in this thesis assigns an H^2(G,U(1)) index to split states.

Completing the correspondence between split states and gapped ground states would strengthen the classification framework and clarify to what extent the index fully captures physically realizable phases.