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Title:
Anomalous transport in spin 1/2 chains
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Abstract:
I will discuss high-temperature spin transport in the integrable XXZ model and its response to next-nearest neighbor (nnn) integrability-breaking spin flips. Our analysis is based on a set of exact sum-rule moment relations, memory funtion Ansaetze and exact diagonalization of small spin chains. In the integrable XXZ model we shall find (i) the regular component of the conductivity to display subleading subballistic low-frequency power law behavior within the gapless phase --- a conjecture regarding the thermodynamic current-carrying states contributing to the ballistic component will also be made; (ii) the isotropic point to be superdiffusive, with a low-frequency power-law exponent equal to −3/7, in close numerical agreement with t-DMRG results; and (iii) a saturating diffusion constant deep into the gapped phase. After breaking integrability we shall find a remarkable sensitivity to the sign of the nnn perturbation: while positive nnn spin flips enhance transport, there is a narrow interval of negative nnn spin-flip amplitudes for which transport becomes subdiffusive. Surprisingly, this sensitivity is absent in the fermionic analogue of the model.
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