Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models

TL;DR

This paper introduces an algebraic bosonization method for (1+1)-dimensional fermionic systems, exemplified through the Heisenberg and Calogero-Sutherland models, linking low-lying excitations to a symmetry algebra and comparing with exact solutions.

Contribution

It presents a novel algebraic bosonization framework based on W_{1+ Infty} symmetry, applied to specific models, providing a new perspective on their excitation structure.

Findings

The approach successfully describes low-lying excitations.

Comparison with Bethe Ansatz solutions validates the method.

The symmetry algebra captures the conservation laws of the models.

Abstract

We propose an approach to treat (1+1)--dimensional fermionic systems based on the idea of algebraic bosonization. This amounts to decompose the elementary low-lying excitations around the Fermi surface in terms of basic building blocks which carry a representation of the W_{1+\infty} \times {\overline W_{1+\infty}} algebra, which is the dynamical symmetry of the Fermi quantum incompressible fluid. This symmetry simply expresses the local particle-number current conservation at the Fermi surface. The general approach is illustrated in detail in two examples: the Heisenberg and Calogero-Sutherland models, which allow for a comparison with the exact Bethe Ansatz solution.