Breakdown of the Chiral Luttinger Liquid in One-Dimension

TL;DR

This paper introduces a fermionic bootstrap method to analyze chiral one-dimensional fermion models, revealing how velocity degeneracy affects Luttinger liquid behavior and leads to the formation of incoherent excitations.

Contribution

It presents a novel fermionic bootstrap approach to study non-bosonizable chiral fermion models and uncovers the impact of velocity changes on Luttinger liquid properties.

Findings

Velocity degeneracy critically influences Luttinger liquid behavior.

A bound state splits off from the continuum when velocity is varied.

Incoherent excitations with linearly growing lifetime emerge.

Abstract

We have developed a fermionic boot-strap method to solve a class of chiral one dimensional fermion model which cannot be tackled by bosonization. Using this scheme, we show that Luttinger liquid behavior in a gas of four interacting chiral Majorana fermions is highly sensitive to the velocity degeneracy. Upon changing the velocity of a one chiral fermion, a sharp bound (or anti-bound) state splits off from the original Luttinger liquid continuum, cutting off the X-ray singularity to form a broad incoherent excitation with a lifetime that grows linearly with frequency.