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

Estienne, Benoît; Bernevig, B. Andrei

doi:10.1016/j.nuclphysb.2011.12.007

Cited by 26 publications

(42 citation statements)

References 40 publications

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“…[26][27][28] In Secs. II B and II C, we give an overview of how both the squeezing algorithm 29,30 and the generalized Pauli principle for spinful states 25 apply to the SSG wave function. In Sec.…”

Section: Statement Of Resultsmentioning

confidence: 99%

“…For instance, in the spin-polarized case, adding the next highest L pseudopotential to the Gaffnian Hamiltonian is known to produce the Haffnian Hamiltonian. 15 Might we be able to generate a "spinHaffnian" state with a Hamiltonian containing positive V 25. Presently we lack a corresponding CFT description with which to conduct the same checks as for the SSG.…”

Section: Discussionmentioning

confidence: 99%

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Spin-singlet Gaffnian wave function for fractional quantum Hall systems

et al. 2013

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We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave functions, namely the non-Abelian spin-singlet state and the nonunitary Gaffnian wave function. This is a spin-singlet generalization of the spin-polarized Gaffnian, which we call the "spin-singlet Gaffnian" (SSG). In this paper we present evidence demonstrating that the SSG corresponds to the ground state of a certain local Hamiltonian, which we explicitly construct, and, further, we provide a relatively simple analytic expression for the unique ground-state wave functions, which we define as the zero energy eigenstates of that local Hamiltonian. In addition, we have determined a certain nonunitary, rational conformal field theory which provides an underlying description of the SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit. In order to verify our construction, we implement two recently proposed techniques for the analysis of fractional quantum Hall trial states: The "spin dressed squeezing algorithm", and the "generalized Pauli principle".

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Section: Statement Of Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Spin-singlet Gaffnian wave function for fractional quantum Hall systems

et al. 2013

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“…The counting of excitations of the series above has been determined through generalized Pauli principles 33,44 . All spinless fermionic (bosonic) many-body wave functions of N e particles can be expressed as linear combinations of Fock states in the occupancy basis of the single-particle…”

Section: Su (C) Fqh Model Wave Functionsmentioning

confidence: 99%

Series of Abelian and non-Abelian states inC>1fractional Chern insulators

et al. 2013

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We report the observation of a new series of Abelian and non-Abelian topological states in fractional Chern insulators (FCI). The states appear at bosonic filling ν = k/(C + 1) (k, C integers) in several lattice models, in fractionally filled bands of Chern numbers C ≥ 1 subject to on-site Hubbard interactions. We show strong evidence that the k = 1 series is Abelian while the k > 1 series is non-Abelian. The energy spectrum at both groundstate filling and upon the addition of quasiholes shows a low-lying manifold of states whose total degeneracy and counting matches, at the appropriate size, that of the Fractional Quantum Hall (FQH) SU (C) (color) singlet k-clustered states (including Halperin, non-Abelian spin singlet(NASS) states and their generalizations). The groundstate momenta are correctly predicted by the FQH to FCI lattice folding. However, the counting of FCI states also matches that of a spinless FQH series, preventing a clear identification just from the energy spectrum. The entanglement spectrum lends support to the identification of our states as SU (C) color-singlets but offers new anomalies in the counting for C > 1, possibly related to dislocations that call for the development of new counting rules of these topological states.

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“…The quasihole excitations, obtained by adding flux quanta, also have zero energy for the (k + 1)-body interaction and can be explicitly constructed. 54,55 The neutral excitations and the quasiparticles of the (k + 1)-body Hamiltonian are nontrivial and do not have zero energy. To construct trial wave functions for them, we generalize Eq.…”

Section: Trial Wave Functionsmentioning

confidence: 99%

“…The quasihole states, obtained by adding flux, are also exact zero-energy states of H con 2 , whose counting can be predicted in several ways and the wave functions are also known exactly. 54,55 Exact solutions are not known for the neutral excitations and the quasiparticles, which do not have zero energy with respect to H con 2 . For these we use the trial wave functions…”

Section: Bosons At Fractional Fillingsmentioning

confidence: 99%

Quantum Hall effect of two-component bosons at fractional and integral fillings

Jain

2013

Phys. Rev. B

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We investigate the feasibility of many candidate quantum Hall states for two-component bosons in the lowest Landau level. We identify interactions for which spin-singlet incompressible states occur at filling factors ν = 2/3, 4/5, and 4/3, and partially spin-polarized states at filling factors 3/4 and 3/2, where "spin" serves as a generic label for the two components. We study ground states, excitations, edge states, and entanglement spectrum for systems with up to 16 bosons and construct explicit trial wave functions to clarify the underlying physics. The composite fermion theory very accurately describes the ground states as well as excitations at ν = 2/3, 4/5, and 3/4, although it is less satisfactory for the ν = 3/2 state. For ν = 4/3 a "non-Abelian spin-singlet" state, which is the exact ground state of a three-body contact interaction, has been proposed to occur even for a two-body contact interaction; our trial wave functions are very accurate for the excitations of the three-body interaction, but they do not describe the excitations of the two-body interaction very well. Instead, we find that the ν = 4/3 state is more likely to be a spin-singlet state of reverse-flux-attached composite fermions at filling ν * = 4. We also consider incompressible states at integral filling factors ν = 1 and 2. The incompressible state at ν = 1 is shown to be well described by the parton-based Jain spin-singlet wave function, and the incompressible state at ν = 2 as the spin-singlet state of reverse-flux-attached composite fermions at ν * = 2, which provides an example of the bosonic integer topological phase.

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

Cited by 26 publications

References 40 publications

Spin-singlet Gaffnian wave function for fractional quantum Hall systems

Spin-singlet Gaffnian wave function for fractional quantum Hall systems

Series of Abelian and non-Abelian states inC>1fractional Chern insulators

Quantum Hall effect of two-component bosons at fractional and integral fillings

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