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Lieb-Schultz-Mattis theorem for quasitopological systems

Freedman, Michael and Nayak, Chetan and Shtengel, Kirill (2008) Lieb-Schultz-Mattis theorem for quasitopological systems. Physical Review B, 78 (17). Art. No. 174411. ISSN 1098-0121. doi:10.1103/PhysRevB.78.174411.

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In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of local operators are short-ranged; and correlation functions of certain nonlocal operators are critical. A variational argument shows gaplessness with ω ∝ k^2 at critical points defined by the absence of certain terms in the Hamiltonian, which is remarkable because equal-time correlation functions of local operators remain short ranged. We call such critical points, in which spatial and temporal scaling are radically different, quasitopological. When these terms are present in the Hamiltonian, the models are in gapped topological phases which are of special interest in the context of topological quantum computation.

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Additional Information:© 2008 The American Physical Society. (Received 31 August 2005; revised 5 August 2008; published 11 November 2008) The authors would like to thank Oded Schramm for illuminating discussions on the statistical properties of critical configurations. We are also thankful to Matthew Hastings for pointing out a gap in the proof presented in the earlier version of this manuscript. In addition, we would like to acknowledge the hospitality of KITP and the Aspen Center for Physics. C.N. and K.S. have been supported by the ARO under Grant No. W911NF-04–1–0236. C.N. has also been supported by the NSF under Grant No. DMR-0411800.
Funding AgencyGrant Number
Army Research OfficeW911NF-04–1–0236
National Science FoundationDMR-0411800
Subject Keywords:critical points; ground states; Ising model; spin Hamiltonians; topology
Issue or Number:17
Record Number:CaltechAUTHORS:FREprb08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12409
Deposited By: Archive Administrator
Deposited On:24 Nov 2008 18:03
Last Modified:08 Nov 2021 22:28

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