Non-Abelian fractional quantum Hall states for hard-core bosons in one dimension.

I present a family of one-dimensional bosonic liquids analogous to non-Abelian fractional quantum Hall states. A new quantum number is introduced to characterize these liquids, the chiral momentum, which differs from the usual angular or linear momentum in one dimension. As their two-dimensional counterparts, these liquids minimize a ¿-body hard-core interaction with the minimum total chiral momentum. They exhibit global order, with a hidden organization of the particles in k identical copies of a one-dimensional Laughlin state. For k = 2 the state is a p-wave paired phase corresponding to the Pfaffian quantum Hall state. By imposing conservation of the total chiral momentum, an exact parent Hamiltonian is derived which involves long-range tunnehng and interaction processes with an amplitude decaying with the chord distance. This family of non-AbeUan liquids is shown to be in formal correspondence with a family of spin-j liquids which are total singlets made out of k indistinguishable resonating valence bond states. The corresponding spin Hamiltonians are obtained. [ABSTRACT FROM AUTHOR]