Filling the Bose sea

doi:10.1088/0305-4470/38/3/006

Filling the Bose sea: symmetric quantum Hall edge states and affine characters

Eddy Ardonne et al 2005 J. Phys. A: Math. Gen. 38 617-636 doi: 10.1088/0305-4470/38/3/006

PDF (234 KB) | References | Articles citing this article

Eddy Ardonne¹, Rinat Kedem² and Michael Stone¹
¹ Department of Physics, University of Illinois, 1110 W Green St, Urbana, IL 61801, USA
² Department of Mathematics, University of Illinois, 1409 W Green St, Urbana, IL 61801, USA
E-mail: ardonne@uiuc.edu, rinat@uiuc.edu and m-stone5@uiuc.edu

Abstract. We explore the structure of the bosonic analogues of the k-clustered 'parafermion' quantum Hall states. We show how the many-boson wavefunctions of k-clustered quantum Hall droplets appear naturally as matrix elements of ladder operators in integrable representations of the affine Lie algebra $\widehat{su}(2)_k$ . Using results of Feigin and Stoyanovsky, we count the dimensions of spaces of symmetric polynomials with given k-clustering properties and show that as the droplet size grows the partition function of its edge excitations evolves into the character of the representation. This confirms that the Hilbert space of edge states coincides with the representation space of the $\widehat{su}(2)_k$ edge-current algebra. We also show that a spin-singlet, two-component k-clustered boson fluid is similarly related to integrable representations of $\widehat{su}(3)$ . Parafermions are not necessary for these constructions.

PACS numbers: 03.65.Fd, 02.20.Tw, 73.43.Cd

Mathematics Subject Classification: 81R10, 17B65

Print publication: Issue 3 (21 January 2005)
Received 23 September 2004, in final form 12 November 2004
Published 23 December 2004

Post to CiteUlike |

Post to Connotea |

Post to Bibsonomy

Filling the Bose sea: symmetric quantum Hall edge states and affine characters

Find related articles

Article options

Authors & Referees