New Vacuum of Bethe Ansatz Solutions in Thirring Model

TL;DR

This paper discovers a new, lower-energy vacuum in the massless Thirring model that breaks chiral symmetry, analyzes its energy spectrum, and critiques the standard bosonization approach for missing zero modes.

Contribution

It introduces a novel vacuum state in the massless Thirring model and provides analytical expressions for the vacuum and excited states, revealing limitations in existing bosonization methods.

Findings

New vacuum breaks chiral symmetry and has lower energy.

Finite energy gap in one particle-one hole states.

Identifies missing zero mode in bosonization procedure.

Abstract

We find a new vacuum of the Bethe ansatz solutions in the massless Thirring model. This vacuum breaks the chiral symmetry and has the lower energy than the well-known symmetric vacuum energy. Further, we evaluate the energy spectrum of the one particle-one hole ($1p-1h$) states, and find that it has a finite gap. The analytical expressions for the true vacuum as well as for the lowest $1p-1h$ excited state are also found. Further, we examine the bosonization of the massless Thirring model and prove that the well-known procedure of bosonization of the massless Thirring model is incomplete because of the lack of the zero mode in the boson field.