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Correlation length versus gap in frustration-free systems

Gosset, David and Huang, Yichen (2016) Correlation length versus gap in frustration-free systems. Physical Review Letters, 116 (9). Art. No. 097202. ISSN 0031-9007. doi:10.1103/PhysRevLett.116.097202.

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Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap ε has correlation length ξ upper bounded as ξ=O(1/ε). In general this bound cannot be improved. Here we study the scaling of the correlation length as a function of the spectral gap in frustration-free local Hamiltonians, and we prove a tight bound ξ=O(1/√ε) in this setting. This highlights a fundamental difference between frustration-free and frustrated systems near criticality. The result is obtained using an improved version of the combinatorial proof of correlation decay due to Aharonov, Arad, Vazirani, and Landau.

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Additional Information:© 2016 American Physical Society. Received 30 October 2015; published 3 March 2016. We thank Spiros Michalakis and John Preskill for interesting discussions. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant No. PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-12500028
Issue or Number:9
Record Number:CaltechAUTHORS:20160208-140901112
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64307
Deposited By: Ruth Sustaita
Deposited On:08 Feb 2016 22:20
Last Modified:10 Nov 2021 23:29

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