Conservation and persistence of spin currents and their relation to the Lieb-Schulz-Mattis twist operators

Abstract

Systems with spin-orbit coupling do not conserve "bare" spin current $\mathbf{j}$. A recent proposal for a conserved spin current $\mathbf{J}$ [J. Shi {\it et.al} Phys. Rev. Lett. {\bf 96}, 076604 (2006)] does not flow persistently in equilibrium. We suggest another conserved spin current $\bar{\mathbf{J}}$ that may flow persistently in equilibrium. We give two arguments for the instability of persistent current of the form $\mathbf{J}$: one based on the equations of motions and another based on a variational construction using Lieb-Schulz-Mattis twist operators. In the absence of spin-orbit coupling, the three forms of spin current coincide.

5 pages; added references, simplified notation, clearer introduction

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