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

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.

arXiv comment12 pages, 12 figs. Long version of cond-mat/9812441

References in corpus (8)

• Renormalization Group Approach to Interacting Fermions
• Bosonization and Fermion Liquids in Dimensions Greater Than One
• The N-chain Hubbard Model in Weak Coupling
• Pedestrian Approach to the Two-Channel Kondo Model
• Bosonization of interacting fermions in arbitrary dimension beyond the Gaussian approximation
• Doping of a spin-1 chain: integrable model
• Marginal Fermi Liquid in a lattice of three-body bound-states
• Breakdown of the Chiral Luttinger Liquid in One-Dimension