TY - JOUR
T1 - Kinetic Theory of Spin Diffusion and Superdiffusion in XXZ Spin Chains
AU - Gopalakrishnan, Sarang
AU - Vasseur, Romain
N1 - Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/3/26
Y1 - 2019/3/26
N2 - 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)∼t1/3. 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.
AB - 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)∼t1/3. 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.
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U2 - 10.1103/PhysRevLett.122.127202
DO - 10.1103/PhysRevLett.122.127202
M3 - Article
C2 - 30978065
AN - SCOPUS:85064038288
SN - 0031-9007
VL - 122
JO - Physical review letters
JF - Physical review letters
IS - 12
M1 - 127202
ER -