Exact Critical Properties of the Multi-Component Interacting Fermion Model with Boundaries

TL;DR

This paper derives exact critical properties and surface exponents for a one-dimensional SU(N) interacting fermion model with boundaries, using Bethe ansatz and boundary conformal field theory, with potential applications to quantum Hall edge states.

Contribution

It provides the first exact determination of surface critical exponents for the SU(N) fermion model with boundaries, linking Bethe ansatz results to boundary conformal field theory.

Findings

Derived surface critical exponents for correlation functions.

Classified exponents into chiral SU(N) Tomonaga-Luttinger liquid and orthogonality catastrophe types.

Discussed implications for photoemission in fractional quantum Hall edge states.

Abstract

Exact critical properties of the one-dimensional SU($N$) interacting fermion model with open boundaries are studied by using the Bethe ansatz method. We derive the surface critical exponents of various correlation functions using boundary conformal field theory. They are classified into two types, i.e. the exponents for the chiral SU($N$) Tomonaga-Luttinger liquid and those related to the orthogonality catastrophe. We discuss a possible application of the results to the photoemission (absorption) in the edge state of the fractional quantum Hall effect.