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Slowest local operators in quantum spin chains

Author(s): Kim, Hyungwon; Bañuls, Mari Carmen; Cirac, J Ignacio; Hastings, Matthew B; Huse, David A

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Abstract: We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to M consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian. We first show that the Frobenius norm bounds the time scale of relaxation of the operator at high temperatures. We find operators with significantly slower relaxation than the slowest simple “hydrodynamic” mode due to energy diffusion. Then we examine some properties of the nontrivial slow operators. Using both exhaustive search and tensor network techniques, we find similar slowly relaxing operators for a Floquet spin chain; this system is hydrodynamically “trivial,” with no conservation laws restricting their dynamics. We argue that such slow relaxation may be a generic feature following from locality and unitarity.
Publication Date: Jul-2015
Electronic Publication Date: 22-Jul-2015
Citation: Kim, Hyungwon, Bañuls, Mari Carmen, Cirac, J Ignacio, Hastings, Matthew B, Huse, David A. (2015). Slowest local operators in quantum spin chains. Physical Review E, 92 (1), 10.1103/PhysRevE.92.012128
DOI: doi:10.1103/PhysRevE.92.012128
ISSN: 1539-3755
EISSN: 1550-2376
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review E
Version: Author's manuscript

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