%0 Journal Article
%T Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature
%A J. M. P. Carmelo
%A T. Prosen
%A D. K. Campbell
%J Physics
%D 2014
%I arXiv
%X 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 $T>0$.
%U http://arxiv.org/abs/1407.0732v2