Elementary Excitations in Gapped Quantum Spin Systems

Autor(en)

Jutho Haegeman, Spyridon Michalakis, Bruno Nachtergaele, Tobias J. Osborne, Norbert Schuch, Frank Verstraete

Abstrakt

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.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Ghent University , California Institute of Technology (Caltech), University of California, Davis, Gottfried Wilhelm Leibniz Universität Hannover, Rheinisch-Westfälische Technische Hochschule Aachen

Journal

Physical Review Letters

Band

111

Anzahl der Seiten

5

ISSN

0031-9007

DOI

https://doi.org/10.1103/PhysRevLett.111.080401

Publikationsdatum

08-2013

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik, 103026 Quantenoptik

Schlagwörter

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/7e27c1c0-069b-42e0-bc04-2c4bb3588180