Model Wave Functions for the Collective Modes and the Magnetoroton Theory of the Fractional Quantum Hall Effect

Yang, Bo; Hu, Zi Xiang; Papić, Zlatko; Haldane, F. D. M.

doi:10.1103/physrevlett.108.256807

Cited by 98 publications

(139 citation statements)

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“…It is expected that the energy gap for both even N and odd N will converge to the same value in the thermodynamic limit. Indeed each N sector should exhibit on the torus two types of neutral excitation modes: a magneto-roton mode 39,40 and a neutral fermion mode 9,40,41 . Their respective dispersion relation should not depend on the particle number parity (as can be seen in Ref.…”

Section: Moore-read State In the Fully Polarized Regimementioning

confidence: 99%

Phase diagram ofν=12+12bilayer bosons with interlayer couplings

et al. 2016

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We present the quantitative phase diagram of the bilayer bosonic fractional quantum Hall system on the torus geometry at total filling factor ν = 1 in the lowest Landau level. We consider short-range interactions within and between the two layers, as well as the inter-layer tunneling. In the fully polarized regime, we provide an updated detailed numerical analysis to establish the presence of the Moore-Read phase of both even and odd numbers of particles. In the actual bilayer situation, we find that both inter-layer interactions and tunneling can provide the physical mechanism necessary for the low-energy physics to be driven by the fully polarized regime, thus leading to the emergence of the Moore-Read phase. Inter-layer interactions favor a ferromagnetic phase when the system is SU (2) symmetric, while the inter-layer tunneling acts as a Zeeman field polarizing the system. Besides the Moore-Read phase, the (220) Halperin state and the coupled Moore-Read state are also realized in this model. We study their stability against each other.

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Section: Moore-read State In the Fully Polarized Regimementioning

confidence: 99%

Phase diagram ofν=12+12bilayer bosons with interlayer couplings

et al. 2016

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“…Very recently, Haldane has proposed a drastically different interpretation of the magneto-roton [6][7][8]. He argues that there is a dynamic degree of freedom in FQH systems which can be interpreted as an internal metric.…”

Section: Introductionmentioning

confidence: 99%

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Golkar

Nguyen

Son

2016

J. High Energ. Phys.

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We consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρ T (ω) andρ T (ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q 4 coefficient of the static structure factor S 4 , and the high-frequency shear modulus of the ground state µ ∞ , which is precisely defined. We confirm an inequality, first suggested by Haldane, that S 4 is bounded from below by |S − 1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin's absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.

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“…(2), though all the modes seem to merge together into the continuum in the long wavelength limit. We want to emphasize that states in this continuum consists of one quasielectron-quasihole pair [12], distinguishing them from the multi-roton continuum starting at an energy double the roton-minimum gap [13], which involves two quasielectrons. These additional neutral excitations are buried in the multi-roton continuum, and in the thermodynamic limit the number of single-pair neutral excitations is also macroscopic.…”

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confidence: 99%

“…where |ψ s i is the set of all basis squeezed from the root configuration [11] in (1) with at most one of the first two orbitals occupied; |ψ J is the state corresponding to fermionic Jack polynomial J −2 000001001001001··· , with an "admissible" root configuration obtained by annihilating the first two electrons (in orbitals labeled 0 and 1) of the root configuration of (1); the coefficients α i and β can be uniquely fixed [12] by imposing the highest weight condition L + |ψ qe Ne/2 = 0, where L + is the raising operator of the total L z on the sphere. It is noteworthy that for a basis derived in this way from such a root configuration, application of the highest-weight condition leads to a highly-overdetermined set of linear equations, which nevertheless have a (unique) solution.…”

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confidence: 99%

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Nature of Quasielectrons and the Continuum of Neutral Bulk Excitations in Laughlin Quantum Hall Fluids

Yang

Haldane

2014

Phys. Rev. Lett.

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We construct model wavefunctions for a family of single-quasielectron states supported by the ν = 1/3 fractional quantum Hall (FQH) fluid. The charge e * = e/3 quasielectron state is identified as a composite of a charge-2e * quasiparticle and a −e * quasihole, orbiting around their common center of charge with relative angular momentum n > 0, and corresponds precisely to the "composite fermion" construction based on a filled n = 0 Landau level plus an extra particle in level n > 0. An effective three-body model (one 2e * quasiparticle and two −e * quasiholes) is introduced to capture the essential physics of the neutral bulk excitations.PACS numbers: 73.43. Lp, 71.10.Pm Elementary excitations of the fractional quantum Hall (FQH) fluids not only are the building blocks of the multi-component FQH states, they also form neutral bound states with an energy gap that characterizes FQH incompressibility. In the Abelian ν = 1/m Laughlin FQH states[1], the quasihole states correspond to insertion of an extra flux quanta through the two-dimensional "Hall surface", and are well-understood. Quasielectron excitations require addition of both electrons and flux quanta, and are in general more complex (i.e. one cannot take quasielectrons as "anti-particles" of quasiholes).A model wavefunction for a single quasielectron was first proposed by Laughlin[1], and was later improved by Jain [2]. In Jain's "composite fermion" (CF) picture, the FQH state is described as an integer quantum Hall (IQHE) state of CFs (electron-vortex composites) in an effective magnetic field, where they fill in what Jain has called "Λ-levels" (ΛLs) [3]. A model CF wavefunction for a lowest-Landau-level (LLL) FQH state is obtained by multiplying the corresponding Slater determinant IQHE state by an even power of the Vandermonde determinant, followed by projection into the LLL. The IQHE state corresponding to the n = 1 ΛL quasielectron state of Ref.[2] corresponds to a filled LLL plus a single electron in the second (n = 1) Landau level. This description of quasielectron states has been reformulated in the formalisms of conformal field theory [4,5] and that of Jack polynomials[6]: though both these descriptions seem very different from that of Ref.[2], all three constructions turn out to produce identical quasielectron states.Model quasielectron states where the extra CF is placed in a higher (n > 1) ΛL were recently used in the construction[8] of "CF excitons" consisting of a quasielectron-quasihole bound state [8], in an attempt to explain experimental inelastic light-scattering observations [9] that were interpreted as the splitting of the neutral bulk excitation spectrum at long wavelengths. Placing the extra CF in different ΛLs leads to different species of exciton states. Most constructions of the quasielectron wavefunctions are implemented in the spherical geometry [7], where many-particle states are characterized by a total angular-momentum quantum number L, and FQH ground states havewhere N e is the number of electrons, while neutral excitation...

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Model Wave Functions for the Collective Modes and the Magnetoroton Theory of the Fractional Quantum Hall Effect

Cited by 98 publications

References 20 publications

Phase diagram ofν=12+12bilayer bosons with interlayer couplings

Phase diagram ofν=12+12bilayer bosons with interlayer couplings

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Nature of Quasielectrons and the Continuum of Neutral Bulk Excitations in Laughlin Quantum Hall Fluids

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