CRITICALITY WITHOUT FRUSTRATION FOR QUANTUM SPIN-1 CHAINS

Type: Book-Chapter

Publication Date: 2013-10-01

Citations: 6

DOI: https://doi.org/10.1142/9789814449243_0053

Abstract

XVIIth International Congress on Mathematical Physics, pp. 542 (2013) No AccessCRITICALITY WITHOUT FRUSTRATION FOR QUANTUM SPIN-1 CHAINSS. BRAVYIS. BRAVYIIBM Thomas J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USAhttps://doi.org/10.1142/9789814449243_0053Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled can the ground state of a FF quantum spin-s chain with nearest-neighbor interactions be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s = 1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right parentheses separated by empty spaces. Entanglement entropy of one half of the chain scales as ½ log (n) + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest. Note from Publisher: This article contains the abstract only. Keywords: Quantum phase transitionsentanglement area lawDyck paths FiguresReferencesRelatedDetails XVIIth International Congress on Mathematical PhysicsMetrics History KeywordsQuantum phase transitionsentanglement area lawDyck pathsPDF download

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