Structure of spinful quantum Hall states: A squeezing perspective

Ardonne, Eddy; Regnault, Nicolas

doi:10.1103/physrevb.84.205134

Cited by 30 publications

(44 citation statements)

References 77 publications

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“…Similar to the previous cases, the universal information in the PES spectrum-the counting of levels per momentum sector-is in agreement with the independently obtained data in Ref. [64] on the sphere. In this case, the bipartition of the system is obtained by fixing the cut such that there are l A ¼ 4 orbitals in part A.…”

Section: Nass Statesupporting

confidence: 80%

“…[39]. The latter state, Φ 221 , has been addressed by Ardonne and Regnault [64], who computed some of its properties by identifying its root configuration on the sphere and deriving its "squeezing" properties. Here, we show how to write down the parent Hamiltonian for these two states for the cylinder and torus geometry.…”

Section: Halperin Permanent Statesmentioning

confidence: 99%

“…According to Ref. [64], the NASS wave function ought to vanish quadratically when we bring together k þ 1 particles of the same spin, and linearly for k þ 1 particles of different spins. For SU (2) …”

Section: Nass Statementioning

confidence: 99%

“…The Hamiltonians for these states have previously been written down for the sphere (or disk) geometry, which we now extend to the cylinder and torus. Furthermore, we propose the parent Hamiltonian for a certain type of state involving the permanent state ("221 times permanent" state [64]), for which the Hamiltonian was previously unknown.…”

Section: B Spinful Statesmentioning

confidence: 99%

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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: Nass Statesupporting

confidence: 80%

Section: Halperin Permanent Statesmentioning

confidence: 99%

Section: Nass Statementioning

confidence: 99%

Section: B Spinful Statesmentioning

confidence: 99%

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Geometric Construction of Quantum Hall Clustering Hamiltonians

2015

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“…We have verified the thin torus wavefunctions by performing exact diagonalization of the model Hamiltonian in the thin-torus limit [115]. .…”

Section: A the Interlayer-pfaffian Statementioning

confidence: 99%

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

et al. 2015

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Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two sub-bands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν = 1/3 + 1/3. We first consider the Coulomb interaction at bilayer separation d, bilayer tunneling energy ∆SAS, and individual layer width w, where we find a phase diagram which includes three competing Abelian phases: a bilayer-Laughlin phase (two nearly decoupled ν = 1/3 layers); a bilayer-spin singlet phase; and a bilayer-symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases have also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν = 1/3 + 1/3 systems merit further experimental study. CONTENTS

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Spin-singlet quantum Hall states and Jack polynomials with a prescribed symmetry

Estienne

Bernevig

2012

Nuclear Physics B

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We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wavefunctions and their quasi-hole excitations can be written in terms of Jack polynomials with a prescribed symmetry. Our approach describes new spin-singlet quantum Hall states at filling fraction ν = 2k 2r−1 and generalizes the (k, r) spin-polarized Jack polynomial states. The NASS and Halperin spin singlet states emerge as specific cases of our construction. The polynomials express many-body states which contain configurations obtained from a root partition through a generalized squeezing procedure involving spin and orbital degrees of freedom. The corresponding generalized Pauli principle for root partitions is obtained, allowing for counting of the quasihole states. We also extract the central charge and quasihole scaling dimension, and propose a conjecture for the underlying CFT of the (k, r) spin-singlet Jack states.arXiv:1107.2534v1 [cond-mat.str-el]

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Structure of spinful quantum Hall states: A squeezing perspective

Cited by 30 publications

References 77 publications

Geometric Construction of Quantum Hall Clustering Hamiltonians

Geometric Construction of Quantum Hall Clustering Hamiltonians

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

Spin-singlet quantum Hall states and Jack polynomials with a prescribed symmetry

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