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

Sarang Gopalakrishnan, Romain Vasseur, Brayden Ware

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)16250-16255
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number33
StatePublished - Aug 13 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General


  • Anomalous diffusion
  • Integrable systems
  • Matrix product operators
  • Spin transport


Dive into the research topics of 'Anomalous relaxation and the high-temperature structure factor of XXZ spin chains'. Together they form a unique fingerprint.

Cite this