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Elementary Excitations in Gapped Quantum Spin Systems

Haegeman, Jutho and Michalakis, Spyridon and Nachtergaele, Bruno and Osborne, Tobias J. and Schuch, Norbert and Verstraete, Frank (2013) Elementary Excitations in Gapped Quantum Spin Systems. Physical Review Letters, 111 (8). Art. No. 080401. ISSN 0031-9007.

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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.

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Additional Information:© 2013 American Physical Society. Received 14 June 2013; published 19 August 2013. Discussions with Karel Van Acoleyen and Henri Verschelde are gratefully acknowledged. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250 and by the AFOSR Grant No. FA8750-12-2-0308 (S. M.), the National Science Foundation under Grant No. DMS-1009502 (B. N.), the Alexander von Humboldt Foundation (N. S.), an Odysseus Grant from the FWO Flanders (F.V. and J. H.), the FWF Grants FoQuS and Vicom (F.V.), the ERC Grants QUERG (F.V.) and QFTCMPS (T. J. O.), and by the Cluster of Excellence EXC 201 Quantum Engineering and Space- Time Research (T. J. O.).
Group:IQIM, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Air Force Office of Scientific Research (AFOSR)FA8750-12-2-0308
Alexander von Humboldt FoundationUNSPECIFIED
FWO Flanders Odysseus GrantUNSPECIFIED
Cluster of Excellence EXC 201 Quantum Engineering and Space Time Research UNSPECIFIED
Classification Code:PACS: 05.30.-d, 03.65.-w, 75.10.Jm
Record Number:CaltechAUTHORS:20130924-103014556
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41498
Deposited By: Tony Diaz
Deposited On:24 Sep 2013 18:09
Last Modified:11 Oct 2013 23:00

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