Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin, Moore-Read, and Read-Rezayi wave functions, belong to a special class of orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant). This fundamental observation allows one 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 wave functions 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.

Unified Fock space representation of fractional quantum Hall states / DI GIOACCHINO, Andrea; Molinari, L. G.; Erba, V.; Rotondo, Pietro. - In: PHYSICAL REVIEW. B. - ISSN 2469-9950. - 95:24(2017). [10.1103/PhysRevB.95.245123]

Unified Fock space representation of fractional quantum Hall states

L.G. Molinari;ROTONDO, PIETRO
2017-01-01

Abstract

Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin, Moore-Read, and Read-Rezayi wave functions, belong to a special class of orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant). This fundamental observation allows one 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 wave functions 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.
2017
Unified Fock space representation of fractional quantum Hall states / DI GIOACCHINO, Andrea; Molinari, L. G.; Erba, V.; Rotondo, Pietro. - In: PHYSICAL REVIEW. B. - ISSN 2469-9950. - 95:24(2017). [10.1103/PhysRevB.95.245123]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2939522
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