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arXiv · 1407.0732

Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature

J. M. P. Carmelo·T. Prosen·D. K. Campbell
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Abstract

Whether at zero spin density $m=0$ and finite temperatures $T>0$ the spin stiffness of the spin-$1/2$ $XXX$ chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we provide an exact upper bound on the stiffness within a canonical ensemble at any fixed value of spin density $m$ and show that it is proportional to $m^2 L$ in the thermodynamic limit of chain length $L\to\infty$, for any finite, nonzero temperature. Moreover, we explicitly compute the stiffness at $m=0$ and confirm that it vanishes. This allows us to exactly exclude the possibility of ballistic transport within the canonical ensemble for $T>0$.

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J. M. P. Carmelo, T. Prosen, D. K. Campbell. 2014-07-02. Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature. https://arxiv.org/abs/1407.0732

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