Slater Decomposition of Laughlin States

Abstract

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 the density operator it is possible to identify individual dominant Slater states of the correct uniform bulk density and filling fraction in the physically relevant $N\to \infty$ limit.

31pp, LaTeX, 5 figures available from author on request, UCONN-93-4

References in corpus (2)

• Large N Limit in the Quantum Hall Effect
• Angular Momentum Distribution Function of the Laughlin Droplet

Cited by in corpus (23)

• Quantum algorithms for quantum chemistry and quantum materials science
• Entanglement entropy in fermionic Laughlin states
• Quantum dots in high magnetic fields: Rotating-Wigner-molecule versus composite-fermion approach
• The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Repulsive Interactions in Quantum Hall Systems as a Pairing Problem
• Fluctuations and Entanglement spectrum in quantum Hall states
• Exact Finite Size Study of the 2dOCP at Gamma=4 and Gamma=6
• Is the Two-Dimensional One-Component Plasma Exactly Solvable?
• Symmetry breaking in Laughlin's state on a cylinder
• On invariant 2x2 β-ensembles of random matrices
• Exact Energy Computation of the One Component Plasma on a Sphere for Even Values of the Coupling Parameter
• Laughlin's function on a cylinder: plasma analogy and representation as a quantum polymer
• Unified Fock space representation of fractional quantum Hall states
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids
• Counter-ion density profile around a charged disk: from the weak to the strong association regime
• The probability distribution of spectral moments for the Gaussian beta-ensembles
• Hyperdeterminantal computation for the Laughlin wave function
• A two-dimensional one component plasma and a test charge : polarization effects and effective potential
• Dyson's Brownian-motion model for random matrix theory - revisited. With an Appendix by Don Zagier
• Construction of a series of new $\nu =2/5$ fractional quantum Hall wave functions by conformal field theory
• Powers of the Vandermonde determinant, Schur Functions, and recursive formulas
• Laughlin states change under large geometry deformations and imaginary time Hamiltonian dynamics