Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 080401 |
| Fachzeitschrift | Physical Review Letters |
| Jahrgang | 111 |
| Ausgabenummer | 8 |
| Publikationsstatus | Veröffentlicht - 19 Aug. 2013 |
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.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
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in: Physical Review Letters, Jahrgang 111, Nr. 8, 080401, 19.08.2013.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Elementary excitations in gapped quantum spin systems
AU - Haegeman, Jutho
AU - Michalakis, Spyridon
AU - Nachtergaele, Bruno
AU - Osborne, Tobias J.
AU - Schuch, Norbert
AU - Verstraete, Frank
PY - 2013/8/19
Y1 - 2013/8/19
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84883188860&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.111.080401
DO - 10.1103/PhysRevLett.111.080401
M3 - Article
AN - SCOPUS:84883188860
VL - 111
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 8
M1 - 080401
ER -