Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published July 16, 2014 | Submitted + Supplemental Material + Published
Journal Article Open

Persistence of locality in systems with power-law interactions

Abstract

Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in D-dimensional lattice models exhibiting 1/r^α interactions with α > D. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, qualitatively reproduce the short- and long-distance dynamical behavior following a local quench in an XY chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verifed in a variety of ultracold-atomic and solid-state systems.

Additional Information

© 2014 American Physical Society. Received 24 January 2014; Published 16 July 2014. Z.-X. G. and M. F.-F. contributed equally to this work. We thank J. Preskill for asking whether the bound derived in Ref. [8] reduces to the nearest-neighbor case as α → ∞, and M. Kastner for pointing out that, if one optimizes with respect to μ at ever r and t in Eq. (2), the hybrid exponential-algebraic behavior shown in Fig. 4 becomes evident only at larger values of α. We thank A. M. Rey, K. Hazzard, C. Monroe, L.-M. Duan, C. Senko, P. Richerme, M. Maghrebi, A. Daley, J. Schachenmayer, A. Lee, J. Smith, and S. Manmana for discussions. This work was supported by the JQI and the NSF PFC at JQI. M. F.-F. thanks the NRC for support. S. M. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250.

Attached Files

Published - PhysRevLett.113.030602.pdf

Submitted - 1401.6174v2.pdf

Supplemental Material - Supp.pdf

Files

Supp.pdf
Files (2.6 MB)
Name Size Download all
md5:ac79ffa7d0c8b2ec1db4784282065a77
226.8 kB Preview Download
md5:56b9e8321f64c1dc4d54e10064d22299
413.7 kB Preview Download
md5:d198d51d8b3ead44e071169ba19056c9
1.9 MB Preview Download

Additional details

Created:
August 20, 2023
Modified:
October 26, 2023