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Title: Anomalous relaxation and the high-temperature structure factor of XXZ spin chains

Journal Article · · Proceedings of the National Academy of Sciences of the United States of America
ORCiD logo [1];  [2];  [3]
  1. City Univ. of New York (CUNY), NY (United States). College of Staten Island, and Graduate Center
  2. Univ. of Massachusetts, Amherst, MA (United States)
  3. Univ. of Massachusetts, Amherst, MA (United States); Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical Physics, Clarendon Lab.
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We compute the spin-structure factor of XXZ spin chains in the Heisenberg and gapped (Ising) regimes in the high-temperature limit for nonzero magnetization, within the framework of generalized hydrodynamics, including diffusive corrections. The structure factor shows a hierarchy of timescales in the gapped phase, owing to s-spin magnon bound states (“strings”) of various sizes. Although short strings move ballistically, long strings move primarily diffusively as a result of their collisions with short strings. The interplay between these effects gives rise to anomalous power-law decay of the spin-structure factor, with continuously varying exponents, at any fixed separation in the late-time limit. We elucidate the cross-over to diffusion (in the gapped phase) and to superdiffusion (at the isotropic point) in the half-filling limit. We verify our results via extensive matrix product operator calculations.

Research Organization:
Univ. of Massachusetts, Amherst, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; National Science Foundation (NSF)
Grant/Contract Number:
SC0019168; DMR-1653271; PHY-1748958
OSTI ID:
1557027
Alternate ID(s):
OSTI ID: 1593374
Journal Information:
Proceedings of the National Academy of Sciences of the United States of America, Vol. 116, Issue 33; ISSN 0027-8424
Publisher:
National Academy of SciencesCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging Kardar-Parisi-Zhang scaling in the zero-magnetization limit text January 2020
NMR relaxation in the spin-1 Heisenberg chain text January 2019
Universal spin dynamics in infinite-temperature one-dimensional quantum magnets text January 2019

Figures / Tables (2)

Fig. 1(p. 2)figure Fig. 1
Fig. 2(p. 3)figure Fig. 2

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
spin transport
integrable systems
anomalous diffusion
matrix product operators