Slowest local operators in quantum spin chains

Hyungwon Kim, Mari Carmen Bañuls, J. Ignacio Cirac, Matthew B. Hastings, and David A. Huse
Phys. Rev. E 92, 012128 – Published 22 July 2015

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
5 More
  • Received 24 October 2014
  • Revised 20 May 2015

DOI:https://doi.org/10.1103/PhysRevE.92.012128

©2015 American Physical Society

Authors & Affiliations

Hyungwon Kim1,2, Mari Carmen Bañuls3, J. Ignacio Cirac3, Matthew B. Hastings4,5, and David A. Huse1

  • 1Physics Department, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
  • 3Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
  • 4Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
  • 5Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 92, Iss. 1 — July 2015

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×