Criticality without Frustration for Quantum Spin-1 Chains
Name
Bravyi-2012-Criticality without Frustration for Quantum.pdf
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110.18 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Bravyi, Sergey
Caha, Libor
Movassagh, Ramis
Nagaj, Daniel
Shor, Peter W.
Date Issued
November 2012
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Bravyi, Sergey et al. “Criticality Without Frustration for Quantum Spin-1 Chains.” Physical Review Letters 109.20 (2012). © 2012 American Physical Society
Version
Final published version
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 the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can 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 brackets separated by empty spaces. Entanglement entropy of one half of the chain scales as 1/2 logn + 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.109.207202
