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

TL;DR

This paper explores the hidden duality and instabilities in the lattice version of the spinless Tomonaga-Luttinger Liquid, revealing how quantum fluctuations and chiral modes lead to complex charge and density instabilities.

Contribution

It introduces explicit bosonic operators for local density fluctuations and links the Luttinger liquid to a classical 2D Coulomb gas with a $ heta$-term, uncovering hidden dualities.

Findings

Identification of charge/density instabilities due to competing fluctuations

Explicit construction of bosonic operators for density fluctuations

Connection of Luttinger liquid to 2D Coulomb gas with $ heta$-term

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.