Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain
By V. B. Bulchandani, Romain Vasseur, C. Karrasch, J. Moore. 2017
176 citations recorded by the source corpus.
The anomalous nature of spin transport in the XXZ quantum spin chain has been a topic of theoretical interest for some time. Here, the integrability of the underlying dynamics leads to a ballistic component of the spin current, characterized by a spin Drude weight, which measures the degree of divergence of the zero-frequency spin conductivity. However, this quantity had previously proven to be beyond the reach of standard Bethe ansatz techniques. Here, the authors show that a recently developed hydrodynamic formalism for quantum integrable models may be used to compute the spin Drude weight. They also propose a numerical scheme to obtain hydrodynamic predictions for finite-time energy transport. This suggests that the hydrodynamic approach captures completely the ballistic component that dominates transport at long times and distances in the gapless regime of the XXZ model.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f86542b7c114d5487a4cdf6a29ee91e0408e7dfd
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Lecture notes on Generalised Hydrodynamics (2019, background): “In this sense, it is perhaps appropriate to refer to the GHD equations as “Bethe-Liouville equations” (the name “Bethe-Boltzmann equations” has been proposed [40], before the present understanding came to light).”
- Drude Weight for the Lieb-Liniger Bose Gas (2017, methodology): “These results have been combined with generalized hydrodynamics in order to evaluate exactly these components of the Drude weight [38, 39].”