A general spinful Luttinger liquid with broken P and T but intact PT symmetry gaps out the spin sector, producing an effective spinless Luttinger liquid with asymmetric velocities.
Safi, A dynamic scattering approach for a gated in- teracting wire, The European Physical Journal B - Con- densed Matter and Complex Systems12, 451 (1999)
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Torsion Induced Asymmetric Luttinger Liquids
A general spinful Luttinger liquid with broken P and T but intact PT symmetry gaps out the spin sector, producing an effective spinless Luttinger liquid with asymmetric velocities.