From Luttinger liquids to Luttinger droplets via higher-order bosonization identities

TL;DR

This paper develops generalized bosonization identities to exactly solve one-dimensional fermionic models with spatially varying interactions, leading to the concept of Luttinger droplets that extend traditional Luttinger liquids.

Contribution

The authors derive higher-order bosonization identities and apply them to obtain exact solutions for inhomogeneous Luttinger liquids with position-dependent couplings.

Findings

Exact solutions for Luttinger droplets with spatially varying interactions

Broken translational invariance in correlation functions

Modified relations between excitation velocities

Abstract

We derive generalized Kronig identities expressing quadratic fermionic terms including momentum transfer to bosonic operators and use them to obtain the exact solution for one-dimensional fermionic models with linear dispersion in the presence of position-dependent interactions and scattering potential. In these Luttinger droplets, which correspond to Luttinger liquids with spatial variations or constraints, the position dependences of the couplings break the translational invariance of correlation functions and modify the Luttinger-liquid interrelations between excitation velocities.