The Quantum Steeplechase

TL;DR

This paper introduces the Non-Chiral Bosonization Technique (NCBT) for analyzing a Luttinger liquid with barriers, providing explicit formulas for two-point functions that improve upon traditional methods by handling non-invariance directly.

Contribution

The paper presents NCBT, a novel analytical approach for Luttinger liquids with barriers, enabling explicit Green function calculations without renormalization or numerical methods.

Findings

Derived closed-form formulas for two-point functions in non-invariant systems.

NCBT captures the most singular part of the Green function asymptotically.

Method simplifies analysis compared to traditional RG and numerical approaches.

Abstract

Quantum Steeplechase is the study of a Luttinger liquid (LL) in one dimension in the presence of a finite number of barriers and wells clustered around an origin. The powerful non-chiral bosonization technique (NCBT) is introduced to write down closed formulas for the two-point functions in the sense of the random phase approximation (RPA). Unlike g-ology based methods that are tied to the translationally invariant, free particle basis, the NCBT explicitly makes use of the translationally non-invariant single particle wavefunctions. The present method that provides the most singular part of the asymptotically exact Green function in a closed form, is in contrast to competing methods that require a combination of renormalization group and/or numerical methods in addition to the bosonization techniques.