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The edge states of the recently proposed quantum spin Hall systems constitutea new symmetry class of one-dimensional liquids dubbed the ``helical liquid'',where the spin orientation is determined by the direction of electron motion.We prove a no-go theorem which states that a helical liquid with an odd numberof components cannot be constructed in a purely 1D lattice system. In a helicalliquid with an odd number of components, a uniform gap in the ground state canappear when the time-reversal (TR) symmetry is spontaneously broken byinteractions. On the other hand, a correlated two-particle backscattering termby an impurity can become relevant while keeping the TR invariance. The Kondoeffect in such a liquid exhibits new features in the structure of the screeningcloud.Comment: 4 pages, accepted by Phys. Rev. Let

Helical Liquid and the Edge of Quantum Spin Hall Systems