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

MARIALUISA FRAU, ALBERTO LERDA, STEFANO SCIUTO, GUILLERMO R. ZEMBA

INTERNATIONAL JOURNAL OF MODERN PHYSICS A

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: Singapore; Año: 1997 vol. 12 p. 4611 - 4661

0217-751X

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.