$U(1)$ Chiral Symmetry in One-Dimensional Interacting Electron System with Spin

TL;DR

This paper investigates a one-dimensional spin-dependent electron system, revealing how chiral symmetry influences its critical behavior and phase diagram, using a boundary Thirring model and renormalization group analysis.

Contribution

It introduces a new critical line in the phase diagram of the 1D electron system by analyzing chiral symmetry breaking and boundary interactions.

Findings

Identification of a new critical line via RG analysis.

Chiral symmetry breaking affects boundary degrees of freedom.

Phase diagram is more complex than previously understood.

Abstract

We study a spin dependent Tomonaga-Luttinger model in one dimension, which describes electron transport through a single barrier. Using the Fermi-Bose equivalence in one dimension, we map the model onto a massless Thirring model with a boundary interaction. A field theoretical perturbation theory for the model has been developed and the chiral symmetry is found to play an important role. The classical bulk action possesses a global $U_A(1)^4$ chiral symmetry, since the fermion fields are massless. This global chiral symmetry is broken by the boundary interaction and the bosonic degrees of freedom, corresponding to the chiral phase transformation, become dynamical. They acquire an additional kinetic action from the fermion path integral measure and govern the critical behaviors of physical operators. On the critical line where the boundary interaction becomes marginal, they decouple from the fermi fields. Consequently the action reduces to the free field action, which contains only a fermion bilinear boundary mass term as an interaction term. By a renormalization group analysis, we obtain a new critical line, which differs from the previously known critical lines in the literature. The result of this work implies that the phase diagram of the one dimensional electron system may have a richer structure than previously known.