title: Elementary excitations in gapped quantum spin systems.
abstract: For quantum lattice systems with local interactions, the Lieb-Robinson bound serves as an alternative for the strict causality of relativistic systems and allows the proof of many interesting results, in particular, when the energy spectrum exhibits an energy gap. In this Letter, we show that for translation invariant systems, simultaneous eigenstates of energy and momentum with an eigenvalue that is separated from the rest of the spectrum in that momentum sector can be arbitrarily well approximated by building a momentum superposition of a local operator acting on the ground state. The error satisfies an exponential bound in the size of the support of the local operator, with a rate determined by the gap below and above the targeted eigenvalue. We show this explicitly for the Affleck-Kennedy-Lieb-Tasaki model and discuss generalizations and applications of our result.
authors.affiliation: Department of Physics and Astronomy, Ghent University, B-9000 Ghent, Belgium.
authors.forename: Jutho
authors.initials: J
authors.lastname: Haegeman
authors.forename: Spyridon
authors.initials: S
authors.lastname: Michalakis
authors.forename: Bruno
authors.initials: B
authors.lastname: Nachtergaele
authors.forename: Tobias J
authors.initials: TJ
authors.lastname: Osborne
authors.forename: Norbert
authors.initials: N
authors.lastname: Schuch
authors.forename: Frank
authors.initials: F
authors.lastname: Verstraete