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The extended conformal theory of Luttinger systems

M. Frau, S. Sciuto, Alberto Lerda A, Guillermo R. Zemba

Published Jun 12, 1996• 2 citations
OpenAlex

Abstract

We describe the recently introduced method of algebraic bosonization of the $(1+1)$-dimensional Luttinger systems by discussing in detail the specific case of the Calogero-Sutherland model, and mentioning the hard-core Bose gas. We also compare our findings with the exact Bethe Ansatz results.

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We demonstrate that the exact form-factors of the Calogero-Sutherland model which were recently found in [10] in confirmation of the congectures earlier made by Haldane (Ref. [9]) can be reproduced in the framework of some bosonization procedure in momentum space. This observation implies a possibility of an exact bosonization of this model describing one-dimensional anyons. 1 The Calogero-Sutherland (CS) model [1] of one-dimensional (1D) spinless particles with long-ranged 1/x 2 interaction ( V (x) = π2 λ(λ−1) L 2 (sin πx L)2 in a finite size L system) provides a remarkable example of an exactly solvable system which can be viewed as a continuous deformation away from either ideal Fermi or Bose gas. At special values λ = 1/2, 1 and 2 the original continuous model describes statistics of eigenvalues of random matrices belonging to one of the three Dyson’s ensembles. Recently

•Jan 1, 1994•0 citations
We describe the recently introduced method of algebraic bosonization of the (1+1)(1+1)(1+1)-dimensional Luttinger systems by discussing in detail the specific case of the Calogero-Sutherland model, and mentioning the hard-core Bose gas. We also compare our findings with the exact Bethe Ansatz results.
We propose an approach to treating (1 + 1)-dimensional fermionic systems based on the idea of algebraic bosonization. This amounts to decomposing the elementary low-lying excitations around the Fermi surface in terms of basic building blocks carrying a representation of the [Formula: see text] 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 through two examples: the Heisenberg and Calogero–Sutherland models, which allow comparison with the exact Bethe ansatz solution.
We demonstrate that the exact form-factors of the Calogero-Sutherland model which were recently found in [10] in confirmation of the congectures earlier made by Haldane (Ref. [9]) can be reproduced in the framework of some bosonization procedure in momentum space. This observation implies a possibility of an exact bosonization of this model describing one-dimensional anyons. 1 The Calogero-Sutherland (CS) model [1] of one-dimensional (1D) spinless particles with long-ranged 1/x 2 interaction ( V (x) = π2 λ(λ−1) L 2 (sin πx L)2 in a finite size L system) provides a remarkable example of an exactly solvable system which can be viewed as a continuous deformation away from either ideal Fermi or Bose gas. At special values λ = 1/2, 1 and 2 the original continuous model describes statistics of eigenvalues of random matrices belonging to one of the three Dyson’s ensembles. Recently