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

51 pages, plain LaTeX

References in corpus (6)

• W_{1+\infty} and W(gl_N) with central charge N
• Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal Models
• Classification of Quantum Hall Universality Classes by $W_{1+\infty }$ symmetry
• Luttinger's Theorem and Bosonization of the Fermi Surface
• $W_{1+\infty }$ Dynamics of Edge Excitations in the Quantum Hall Effect
• The $W_{1+\infty }$ effective theory of the Calogero- Sutherland model and Luttinger systems.

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• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• Large N limit of Calogero-Moser models and Conformal Field Theories
• Effective short distance interaction in Calogero-Sutherland quantum fluids
• Laminar flow of charged quantum fluids of the Calogero-Sutherland universality class
• Quantum dynamics of the effective field theory of the Calogero-Sutherland model
• Dynamic structure factor of Calogero-Sutherland fluids
• The extended conformal theory of the Calogero-Sutherland model
• Totally classical Calogero model
• A new class of Matrix Models arising from the W-infinity Algebra
• Bosonic Bogoliubov transformations as Lorentz boosts in $(c,\overline{c})=(1,1)$ conformal field theories with marginal $J\overline{J}$ deformations