Kinetic Theory of Spin Diffusion and Superdiffusion in Spin Chains
Abstract
We address the nature of spin transport in the integrable XXZ spin chain, focusing on the isotropic Heisenberg limit. We calculate the diffusion constant using a kinetic picture based on generalized hydrodynamics combined with Gaussian fluctuations: we find that it diverges, and show that a self-consistent treatment of this divergence gives superdiffusion, with an effective time-dependent diffusion constant that scales as $$D(t) \sim t^{1/3}$$. This exponent had previously been observed in large-scale numerical simulations, but had not been theoretically explained. We briefly discuss XXZ models with easy-axis anisotropy $$\Delta > 1$$. Our method gives closed-form expressions for the diffusion constant $$D$$ in the infinite-temperature limit for all $$\Delta > 1$$. We find that $$D$$ saturates at large anisotropy, and diverges as the Heisenberg limit is approached, as $$D \sim (\Delta - 1)^{-1/2}$$.
- Authors:
-
- City Univ. (CUNY), NY (United States)
- Univ. of Massachusetts, Amherst, MA (United States)
- Publication Date:
- Research Org.:
- Univ. of Massachusetts, Amherst, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1509474
- Grant/Contract Number:
- SC0019168
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 12; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Gopalakrishnan, Sarang, and Vasseur, Romain. Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.122.127202.
Gopalakrishnan, Sarang, & Vasseur, Romain. Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains. United States. https://doi.org/10.1103/PhysRevLett.122.127202
Gopalakrishnan, Sarang, and Vasseur, Romain. Tue .
"Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains". United States. https://doi.org/10.1103/PhysRevLett.122.127202. https://www.osti.gov/servlets/purl/1509474.
@article{osti_1509474,
title = {Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains},
author = {Gopalakrishnan, Sarang and Vasseur, Romain},
abstractNote = {We address the nature of spin transport in the integrable XXZ spin chain, focusing on the isotropic Heisenberg limit. We calculate the diffusion constant using a kinetic picture based on generalized hydrodynamics combined with Gaussian fluctuations: we find that it diverges, and show that a self-consistent treatment of this divergence gives superdiffusion, with an effective time-dependent diffusion constant that scales as $D(t) \sim t^{1/3}$. This exponent had previously been observed in large-scale numerical simulations, but had not been theoretically explained. We briefly discuss XXZ models with easy-axis anisotropy $\Delta > 1$. Our method gives closed-form expressions for the diffusion constant $D$ in the infinite-temperature limit for all $\Delta > 1$. We find that $D$ saturates at large anisotropy, and diverges as the Heisenberg limit is approached, as $D \sim (\Delta - 1)^{-1/2}$.},
doi = {10.1103/PhysRevLett.122.127202},
journal = {Physical Review Letters},
number = 12,
volume = 122,
place = {United States},
year = {Tue Mar 26 00:00:00 EDT 2019},
month = {Tue Mar 26 00:00:00 EDT 2019}
}
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