ar X iv : h ep - t h / 04 10 15 1 v 2 17 J an 2 00 5 DFF 420 - 09 - 04 Matrix Model Description of Laughlin Hall States
نویسنده
چکیده
We analyze Susskind's proposal of applying the non-commutative Chern-Simons theory to the quantum Hall effect. We study the corresponding regularized matrix Chern-Simons theory introduced by Polychronakos. We use holomorphic quantiza-tion and perform a change of matrix variables that solves the Gauss law constraint. The remaining physical degrees of freedom are the complex eigenvalues that can be interpreted as the coordinates of electrons in the lowest Landau level with Laughlin's wave function. At the same time, a statistical interaction is generated among the electrons that is necessary to stabilize the ground state. The stability conditions can be expressed as the highest-weight conditions for the representations of the W-infinity algebra in the matrix theory. This symmetry provides a coordinate-independent characterization of the incompressible quantum Hall states.
منابع مشابه
ar X iv : h ep - t h / 05 09 04 5 v 1 6 S ep 2 00 5 A Bethe Ansatz Study of Free Energy and Excitation Spectrum for even spin Fateev Zamolodchikov Model
A Bethe Ansatz study of a self dual ZN spin model is undertaken for even spin system. One has to solve a coupled system of Bethe Ansatz Equations (BAE) involving zeroes of two families of transfer matrices. A numerical study on finite size lattices is done for identification of elementary excitations over the Ferromagnetic and Antiferromagnetic ground states. The free energies for both Ferromag...
متن کاملar X iv : q ua nt - p h / 02 09 04 5 v 1 5 S ep 2 00 2 Lewenstein - Sanpera Decomposition for 2 ⊗ 2 Systems
As it is well known, every bipartite 2⊗2 density matrix can be obtained from Bell decompos-able states via local quantum operations and classical communications (LQCC). Using this fact, the Lewenstein-Sanpera decomposition of an arbitrary bipartite 2 ⊗ 2 density matrix has been obtained through LQCC action upon Lewenstein-Sanpera decomposition of Bell decomposable states of 2 ⊗ 2 quantum system...
متن کاملar X iv : m at h / 04 09 02 9 v 1 [ m at h . A G ] 2 S ep 2 00 4 ACM BUNDLES ON GENERAL HYPERSURFACES IN P 5 OF LOW DEGREE
In this paper we show that on a general hypersurface of degree r = 3, 4, 5, 6 in P 5 a rank 2 vector bundle E splits if and only if h 1 E(n) = h 2 E(n) = 0 for all n ∈ Z. Similar results for r = 1, 2 were obtained in [15], [16] and [1].
متن کاملar X iv : h ep - t h / 04 09 30 6 v 1 2 9 Se p 20 04 Minimal String Theory ⋆
We summarize recent progress in the understanding of minimal string theory, focusing on the worldsheet description of physical operators and D-branes. We review how a geometric interpretation of minimal string theory emerges naturally from the study of the D-branes. This simple geometric picture ties together many otherwise unrelated features of minimal string theory, and it leads directly to a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005