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

Marialuisa Frau·Alberto Lerda·Stefano Sciuto·Guillermo R. Zemba
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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.

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Marialuisa Frau, Alberto Lerda, Stefano Sciuto, Guillermo R. Zemba. 1996-03-16. Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models. https://doi.org/10.1142/s0217751x97002498

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