Gopalakrishnan Sarang, Vasseur Romain
Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314; Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, New York 10016, USA.
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev Lett. 2019 Mar 29;122(12):127202. doi: 10.1103/PhysRevLett.122.127202.
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)∼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 Δ>1. Our method gives closed-form expressions for the diffusion constant D in the infinite-temperature limit for all Δ>1. We find that D saturates at large anisotropy, and diverges as the Heisenberg limit is approached, as D∼(Δ-1)^{-1/2}.
我们研究了可积XXZ自旋链中的自旋输运性质，重点关注各向同性海森堡极限情况。我们基于广义流体动力学并结合高斯涨落，利用动力学图像计算扩散常数：我们发现它发散，并表明对这种发散进行自洽处理会导致超扩散，其有效时间相关扩散常数的标度为(D(t)\sim t^{1/3})。这个指数此前在大规模数值模拟中被观测到，但尚未得到理论解释。我们简要讨论了易轴各向异性(\Delta>1)的XXZ模型。我们的方法给出了所有(\Delta>1)情况下在无限温度极限下扩散常数(D)的封闭形式表达式。我们发现，在大各向异性时(D)达到饱和，并且在接近海森堡极限时发散，其标度为(D\sim(\Delta - 1)^{-1/2}) 。
