Decomposition of fractional quantum Hall model states: Product rule symmetries and approximations

Thomale, Ronny; Estienne, Benoît; Regnault, Nicolas; Bernevig, B. Andrei

doi:10.1103/physrevb.84.045127

Cited by 56 publications

(69 citation statements)

References 106 publications

(163 reference statements)

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“…[62]. Furthermore, on both the sphere and cylinder, because of the singlet property of the wave function, we expect the PES levels to be multiplets of the S 2 operator [65], as can be verified in Fig. 8.…”

Section: Spin-singlet Gaffnian Statementioning

confidence: 80%

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Geometric Construction of Quantum Hall Clustering Hamiltonians

2015

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Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z 3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SUðnÞ cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.

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Section: Spin-singlet Gaffnian Statementioning

confidence: 80%

“…Thus, the OES on the sphere can be directly compared with the OES on the open cylinder. Finally, for spinful states, the spin quantum number commutes with the reduced density operator of the OES and thus allows for additional resolution of the ES level counting [65].…”

Section: B Spinful Statesmentioning

confidence: 99%

Geometric Construction of Quantum Hall Clustering Hamiltonians

2015

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“…Using this property one can calculate the coecients of fermionic Jacks in the Slater determinant basis [10,11].…”

Section: Fermionic Jack Polynomialsmentioning

confidence: 99%

Mathematical Structure of Bosonic and Fermionic Jack States and Their Application in Fractional Quantum Hall Effect

Kuśmierz

Wójs

2014

Acta Phys. Pol. A

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Fractional quantum Hall eect is a remarkable behaviour of correlated electrons, observed exclusively in two dimensions, at low temperatures, and in strong magnetic elds. The most prominent fractional quantum Hall state occurs at Landau level lling factor ν = 1/3 and it is described by the famous Laughlin wave function, which (apart from the trivial Gaussian factor) is an example of Jack polynomial. Fermionic Jack polynomials also describe another pair of candidate fractional quantum Hall states: MooreRead and ReadRezayi states, believed to form at the ν = 1/2 and 3/5 llings of the second Landau level, respectively. Bosonic Jacks on the other hand are candidates for certain correlated states of cold atoms. We examine here a continuous family of fermionic Jack polynomials whose special case is the Laughlin state as approximate wave functions for the 1/3 fractional quantum Hall eect.

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“…1]. An explicit recursion construction of both Jack and fermionic Jacks was derived [5,10,11,16]. We compare selected Jack-based wave functions with ground states of the Coulomb interaction of electrons confined in given Landau level (LL) and two materials: GaAs and graphene.…”

Section: Introductionmentioning

confidence: 99%

“…The Jack polynomials (Jacks) [1][2][3][4][5][6] have been related to the fractional quantum Hall effect (FQHE) by a number of authors [7][8][9][10][11][12][13][14][15]. The Jack polynomial J α λ is indexed by a real parameter α and a partition λ. Partition is a series of nonnegative integers in a decreasing order.…”

Section: Introductionmentioning

confidence: 99%

Jack Polynomials and Fractional Quantum Hall Effect at ν = 1/3

Kuśmierz

Wójs

2016

Acta Phys. Pol. A

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We investigate properties of strongly correlated, spinless electrons confined within given Landau level at filling factor ν = 1/3. Our analysis is based on the formalism of the Jack polynomials. Selected Jack polynomial wave functions are compared with ground states of the Coulomb interaction Hamiltonians, in different materials and the Landau levels, obtained by exact diagonalization. We show that certain Jack wave functions can be used as a description of fractional quantum Hall states.

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Decomposition of fractional quantum Hall model states: Product rule symmetries and approximations

Cited by 56 publications

References 106 publications

Geometric Construction of Quantum Hall Clustering Hamiltonians

Geometric Construction of Quantum Hall Clustering Hamiltonians

Mathematical Structure of Bosonic and Fermionic Jack States and Their Application in Fractional Quantum Hall Effect

Jack Polynomials and Fractional Quantum Hall Effect at ν = 1/3

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