Bound-State Instability of the Chiral Luttinger Liquid in One-Dimension

TL;DR

This paper introduces a novel bootstrap method for exactly solving certain one-dimensional chiral fermion models, revealing bound-state instabilities that alter the excitation spectrum from traditional Luttinger liquid behavior.

Contribution

The authors develop a new bootstrap approach to solve interacting chiral fermion models with unequal velocities, including the SO(3) model, uncovering bound states and spectral changes.

Findings

Exact solutions for models with unequal Majorana fermion velocities.

Discovery of bound states splitting from the Luttinger liquid continuum.

Spectral broadening with lifetime proportional to frequency.

Abstract

We have developed a new boot-strap method for solving a class of interacting one-dimensional chiral fermions. The conventional model for interacting right-moving electrons with spin has an SO(4) symmetry, and can be written as four interacting Majorana fermions, each with the same velocity. We have found a method for solving some cases when the velocities of these Majorana fermions are no longer equal. We demonstrate in some detail the remarkable result that corrections to the non skeleton self-energy identically vanish for these models, and this enables us to solve them exactly. For the cases where the model can be solved by bosonization, our method can be explicitly checked. However, we are also able to solve some new cases where the excitation spectrum differs qualitatively from a Luttinger liquid. Of particular interest, is the so-called SO(3) model, where a triplet of Majorana fermions moving at one velocity, interact with a single Majorana fermion moving at another velocity. We show using our method, that 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.