Particle-hole symmetry and composite fermions in fractional quantum Hall states

Nguyen, Dung Xuan; Golkar, Siavash; Roberts, Matthew M.; Son, D.

doi:10.1103/physrevb.97.195314

Cited by 31 publications

(55 citation statements)

References 64 publications

(114 reference statements)

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“…(162) and (163) leaves behind the low-energy degrees of freedom L R ρ + L R d1 + L L ψ , where L L ψ is the Lagrangian density for the remaining Majorana fermion ψ L in L L SO (2) in (161). This matches exactly with the Lagrangian densities (25) and (27) for the parton Pfaffian state. This completes the proof of the particle-hole symmetry…”

Section: Particle-hole Symmetry For Partonssupporting

confidence: 81%

Paired parton quantum Hall states: A coupled wire construction

et al. 2019

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The Pfaffian fractional quantum Hall (FQH) states are incompressible non-Abelian topological fluids present in a half-filled electron Landau level, where there is a balanced population of electrons and holes. They give rise to half-integral quantum Hall plateaus that divide critical transitions between integer quantum Hall (IQH) states. On the other hand, there are Abelian FQH states, such as the Laughlin state, that can be understood using partons, which are fermionic divisions of the electron. In this paper, we propose a new family of incompressible paired parton FQH states at filling ν = 1/6 (modulo 1) that emerge from critical transitions between IQH states and Abelian FQH states at filling ν = 1/3 (modulo 1). These paired parton states are originated from a half-filled parton Landau level, where there is an equal amount of partons and holes. They generically support Ising-like anyonic quasiparticle excitations and carry non-Abelian Pfaffian topological orders (TO) for partons. We prove the principle existence of these paired parton states using exactly solvable interacting arrays of electronic wires under a magnetic field. Moreover, we establish a new notion of particle-hole (PH) symmetry for partons and relate the PH symmetric parton Pfaffian TO with the gapped symmetric surface TO of a fractional topological insulator in three dimension. arXiv:1812.01642v1 [cond-mat.str-el]

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Section: Particle-hole Symmetry For Partonssupporting

confidence: 81%

Paired parton quantum Hall states: A coupled wire construction

et al. 2019

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“…If one wishes to treat this equation as a precise prediction, however, one must specify precisely the definition of the Fermi wave vector k F . If one defines k F as the square-root of 4π times the density of composite fermions, which is equal to the density of electrons in HLR but is determined by the density of flux quanta in Son-Dirac, one would find that the wave vectors q given by (33) would agree in the two theories at first order in |∆B| but would disagree at order |∆B| 2 . Furthermore, the HLR result would violate PH symmetry at this order.…”

Section: Hall Conductance At ν = 1/2mentioning

confidence: 99%

“…The sign and magnitude of the observed deviation is such that the data can be well fit by the form (33) with a choice of k F dictated by the density of electrons for ν > 1/2 and by the density of holes for ν < 1/2. This means that if one wishes to fit the data to (33), one should choose k F to satisfy k F l B = [min(2ν, 2 − 2ν)] 1/2 , rather than the value k F = l −1 B predicted by the RPA-type calculations of Refs. 22 and 28.…”

Section: Hall Conductance At ν = 1/2mentioning

confidence: 99%

“…Another quantity that has been predicted to show commensurability oscillations near ν = 1/2 is the spectrum ω(q) of neutral excitations in a quantized Hall state of the form ν = p/(2p + 1), for large values of |p|. The lowest frequency branch is predicted to have a series of minima, known as magnetoroton minima, which occur at wave vectors given by (33) in the limit of large |p| or small |∆B|. 30 As in the case of the Weiss oscillations, a naive application of the HLR theory, in which k F is determined by the density of electrons, would predict a PH asymmetry at order |∆B| 2 .…”

Section: Hall Conductance At ν = 1/2mentioning

confidence: 99%

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The Half-Full Landau Level

Halperin

2020

Fractional Quantum Hall Effects

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At even-denominator Landau level filling fractions, such as ν = 1/2, the ground state, in most cases, has no energy gap, and there is no quantized plateau in the Hall conductance. Nevertheless, the states exhibit non-trivial low-energy phenomena. Open questions concerning the proper description of these systems have attracted renewed attention during the last few years. Issues at ν = 1/2 include consequences of particle-hole symmetry, which should be present for a spin-aligned system in the limit where one can neglect mixing between Landau levels. Other issues concern questions of anisotropy and geometry, properties at non-zero temperature, and effects of relatively strong disorder. In cases where one does find a gapped even-denominator quantized Hall state, such as ν = 5/2 in GaAs structures, major questions have arisen about the nature of the quantum state, which will be discussed briefly in this chapter. The chapter will also discuss phenomena that can occur in a two-component system near half filling, i.e., when the total filling factor νtot is close to 1.

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“…Finally we focus on making sense of the ellipses in (1,2), which stand for potential Maxwell terms. Having analyzed the mapping of the Fermionic hamiltonians, we now show how the Maxwell terms for the A and a fields transform into each other under (23, 24).…”

Section: Maxwell Termsmentioning

confidence: 99%

Antiparticles as Particles: QED2+1 and Composite Fermions at ν=12

Agarwal

2019

Phys. Rev. Lett.

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We present a continuum operator map that inverts the role of particles and antiparticles in three dimensional QED. This is accomplished by the attachment of specific holomorphic Wilson lines to Dirac fermions. We show that this nonlocal map provides a continuum realization of Son's composite fermions at ν = 1 2 . The inversion of Landau levels and the Dirac-cone-composite-Fermion duality is explicitly demonstrated for the case of slowly varying magnetic fields. The role of Maxwell-terms as well as the connection of this construction to a gauge-invariant formulation of 3D gauge theories is also elaborated upon.

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Particle-hole symmetry and composite fermions in fractional quantum Hall states

Cited by 31 publications

References 64 publications

Paired parton quantum Hall states: A coupled wire construction

Paired parton quantum Hall states: A coupled wire construction

The Half-Full Landau Level

Antiparticles as Particles: QED2+1 and Composite Fermions at ν=12

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