Non-chiral bosonization of strongly inhomogeneous Luttinger liquids

TL;DR

This paper introduces non-chiral bosonization (NCBT), a novel method for analyzing strongly inhomogeneous Luttinger liquids, providing exact reproductions of free fermion properties and validating results through perturbation and Schwinger-Dyson equations.

Contribution

The paper develops NCBT, a new formalism that accurately models inhomogeneous Luttinger liquids and confirms its validity via perturbative and non-perturbative checks.

Findings

NCBT reproduces free fermion properties exactly.

Green functions from NCBT match perturbative expansions.

Schwinger-Dyson equation confirms NCBT's non-perturbative validity.

Abstract

Non-chiral bosonization (NCBT) is a non-trivial modification of the standard Fermi-Bose correspondence in one spatial dimensions made in order to facilitate the study of strongly inhomogeneous Luttinger liquids (LL) where the properties of free fermions plus the source of inhomogeneities are reproduced exactly. The formalism of NCBT is introduced and limiting case checks, fermion commutation rules, point splitting constraints, etc. are discussed. The Green functions obtained from NCBT are expanded in powers of the fermion-fermion interaction strength (forward scattering short-range only) and compared with the corresponding terms obtained using standard fermionic perturbation theory. Lastly, the Green functions obtained from NCBT are inserted into the Schwinger-Dyson equation which is the equation of motion of the Green functions and serves as a non-perturbative confirmation of the method. Some other analytical approaches like functional bosonization and numerical techniques like DMRG, which can be used to obtain the correlation functions in 1D, are briefly discussed.