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Title: Kinetic Theory of Spin Diffusion and Superdiffusion in X X Z 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:
 [1];  [2]
  1. City Univ. (CUNY), NY (United States)
  2. 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) (SC-22); 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. doi:10.1103/PhysRevLett.122.127202.
Gopalakrishnan, Sarang, and Vasseur, Romain. Tue . "Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains". United States. doi: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 = {2019},
month = {3}
}

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