Exact effective action for fermions in one dimension with backscattering at a boundary

TL;DR

This paper derives an exact effective action for free Dirac fermions in one dimension with boundary backscattering, including effects of forward scattering and boundary condition twists, with applications to 1D Fermi systems.

Contribution

It provides the first exact effective action for fermions with boundary backscattering, incorporating complex boundary effects and general scattering amplitudes.

Findings

Exact partition function for fermions with boundary conditions

Effective boundary action including backscattering and forward scattering

Connection to boundary Sine-Gordon model for small backscattering

Abstract

We report exact results for the partition function for free Dirac fermions on a half line with physically sensible boundary conditions. An exact effective action for general backscattering amplitudes is derived. The action also includes the effects of both a (time-dependent) forward scattering amplitude and a dynamical chiral twist of the fermion boundary conditions. For a small backscattering amplitude, the effective action has the expected boundary Sine-Gordon form. We discuss applications of our results to one-dimensional Fermi systems with local backscattering.