{
  "id": "1805.06895",
  "version": "v1",
  "published": "2018-05-17T18:00:00.000Z",
  "updated": "2018-05-17T18:00:00.000Z",
  "title": "Emergent locality in systems with power-law interactions",
  "authors": [
    "David J. Luitz",
    "Yevgeny Bar Lev"
  ],
  "comment": "9 pages, 9 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.quant-gas",
    "cond-mat.str-el"
  ],
  "abstract": "Locality imposes stringent constraints on the spreading of information in nonrelativistic quantum systems, which is reminiscent of a \"light-cone,\" a casual structure arising in their relativistic counterparts. Long-range interactions can potentially soften such constraints, allowing almost instantaneous long jumps of particles, thus defying causality. Since interactions decaying as a power-law with distance, $r^{-\\alpha}$, are ubiquitous in nature, it is pertinent to understand what is the fate of causality and information spreading in such systems. Using a numerically exact technique we address these questions by studying the out-of-time-order correlation function of a representative generic system in one-dimension. We show that while the interactions are long-range, their effect on information spreading is asymptotically negligible as long as $\\alpha>1$. In this range we find a complex compound behavior, where after a short transient a fully local behavior emerges, yielding asymptotic \"light-cones\" virtually indistinguishable from \"light-cones\" in corresponding local models. The long-range nature of the interaction is only expressed in the power-law leaking of information from the \"light-cone,\" with the same exponent as the exponent of the interaction, $\\alpha$. Our results directly imply that all previously obtained rigorous bounds on information spreading in long-range interacting systems are not tight, and thus could be improved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-17T18:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power-law interactions",
      "emergent locality",
      "information spreading",
      "locality imposes stringent constraints",
      "light-cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}