Matrix Model Description of Laughlin Hall States
نویسندگان
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 model, the matrix Chern-Simons theory introduced by Polychronakos. Earlier analyses of this theory found several features that are expected in the quantum Hall effect but also raised some doubts. We show that the matrix theory exactly describes the quantum mechanics of electrons in the lowest Landau level with the Laughlin wave function for ground state. We use holomorphic quantization and perform a change of matrix variables that solves the Gauss law constraint and exhibits the particle degrees of freedom.
منابع مشابه
Quantum Hall states as matrix Chern-Simons theory
We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of the quasiparticle number is shown to arise quantum mechanically and to agree with Laughlin theory. We also point out the effective equivalence of this model, and therefore of the quantum Hall system, wi...
متن کاملar 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
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 ...
متن کاملX iv : c on d - m at / 9 30 60 22 v 1 8 J un 1 99 3 Slater Decomposition of Laughlin States ∗ Gerald
The second-quantized form of the Laughlin states for the fractional quantum Hall effect is discussed by decomposing the Laughlin wavefunctions into the N -particle Slater basis. A general formula is given for the expansion coefficients in terms of the characters of the symmetric group, and the expansion coefficients are shown to possess numerous interesting symmetries. For expectation values of...
متن کاملQuantum Hall states on the cylinder as unitary matrix Chern-Simons theory
We propose a unitary matrix Chern-Simons model representing fractional quantum Hall fluids of finite extent on the cylinder. A mapping between the states of the two systems is established. Standard properties of Laughlin theory, such as the quantization of the inverse filling fraction and of the quasiparticle number, are reproduced by the quantum mechanics of the matrix model. We also point out...
متن کاملMatrix Effective Theories of the Fractional Quantum Hall effect
The present understanding of nonperturbative ground states in the fractional quantum Hall effect is based on effective theories of the Jain “composite fermion” excitations. We review the approach based on matrix variables, i.e. D0 branes, originally introduced by Susskind and Polychronakos. We show that the Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of the quantum...
متن کامل