Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
Abstract
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.
- Publication Date:
- Research Org.:
- Univ. of Massachusetts, Amherst, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; National Science Foundation (NSF)
- OSTI Identifier:
- 1557027
- Alternate Identifier(s):
- OSTI ID: 1593374
- Grant/Contract Number:
- SC0019168; DMR-1653271; PHY-1748958
- Resource Type:
- Published Article
- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America
- Additional Journal Information:
- Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 116 Journal Issue: 33; Journal ID: ISSN 0027-8424
- Publisher:
- National Academy of Sciences
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; spin transport; integrable systems; anomalous diffusion; matrix product operators
Citation Formats
Gopalakrishnan, Sarang, Vasseur, Romain, and Ware, Brayden. Anomalous relaxation and the high-temperature structure factor of XXZ spin chains. United States: N. p., 2019.
Web. doi:10.1073/pnas.1906914116.
Gopalakrishnan, Sarang, Vasseur, Romain, & Ware, Brayden. Anomalous relaxation and the high-temperature structure factor of XXZ spin chains. United States. https://doi.org/10.1073/pnas.1906914116
Gopalakrishnan, Sarang, Vasseur, Romain, and Ware, Brayden. Tue .
"Anomalous relaxation and the high-temperature structure factor of XXZ spin chains". United States. https://doi.org/10.1073/pnas.1906914116.
@article{osti_1557027,
title = {Anomalous relaxation and the high-temperature structure factor of XXZ spin chains},
author = {Gopalakrishnan, Sarang and Vasseur, Romain and Ware, Brayden},
abstractNote = {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.},
doi = {10.1073/pnas.1906914116},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 33,
volume = 116,
place = {United States},
year = {2019},
month = {7}
}
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https://doi.org/10.1073/pnas.1906914116
https://doi.org/10.1073/pnas.1906914116
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Cited by: 11 works
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Figures / Tables:
Fig. 1: Return probability. (A) Exponent of the return probability, C(0, t)∼ t−γ , as a function of the filling and the anisotropy. This result applies for any fixed x as t→∞. (B) Mechanism for anomalous local relaxation: The velocity of an s-string in the easy-axis XXZ model decreases exponentiallymore »
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