Journal
PHYSICAL REVIEW LETTERS
Volume 122, Issue 12, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.122.127202
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Funding
- NSF [DMR-1653271]
- U.S. Department of Energy, Office of Science, Basic Energy Sciences [DE-SC0019168]
- U.S. Department of Energy (DOE) [DE-SC0019168] Funding Source: U.S. Department of Energy (DOE)
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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) similar to 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 similar to (Delta - 1)(-1/2).
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