Hidden Duality and associated instabilities of Tomonaga-Luttinger Liquid on Lattice

Abstract

Hidden duality and associated instabilities of the spinless Luttinger liquid on lattice are reported. The local quantum fluctuations and the long-distance chiral modes compete and as a result produce a hierarchy of exotic charge/density instabilities. Explicit bosonic quantum operators for the local density fluctuations are constructed and are used to make identification of the Luttinger liquid with the classical 2D Coulomb gas with $\theta$-term and with the rich hidden duality.