Unified Fock space representation of fractional quantum Hall states

Abstract

Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin, Moore-Read and Read-Rezayi wavefunctions, belong to a special class of orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant). This fundamental observation allows to point out two different recurrence relations for the coefficients of the permanent (Slater) decomposition of the bosonic (fermionic) states. Here we provide an explicit Fock space representation for these wavefunctions by introducing a two-body squeezing operator which represents them as a Jastrow operator applied to reference states, which are in general simple periodic one dimensional patterns. Remarkably, this operator representation is the same for bosons and fermions, and the different nature of the two recurrence relations is an outcome of particle statistics.

arXiv comment10 pages, 3 figures

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Cited by in corpus (6)

• Quantum algorithms for quantum chemistry and quantum materials science
• Creating and manipulating a Laughlin-type $\nu =1/3$ fractional quantum Hall state on a quantum computer with linear depth circuits
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Roadmap for quantum simulation of the fractional quantum Hall effect
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Jack on a Devil's staircase