Random-phase approximation in the fractional-statistics gas

Fetter, Alexander L.; Hanna, Charles B.; Laughlin, R. B.

doi:10.1103/physrevb.39.9679

Cited by 381 publications

(189 citation statements)

References 3 publications

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“…Laughlin and collaborators [156,138,91] found a speciÿc model with long-range four-spin interactions for which his quantum hall wavefunction is the ground state. Therefore, time-reversal and parity are spontaneously broken in this state.…”

Section: The Doped Hubbard Modelmentioning

confidence: 99%

Singular or non-Fermi liquids

2002

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Section: The Doped Hubbard Modelmentioning

confidence: 99%

Singular or non-Fermi liquids

2002

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“…The most successful among the latter has been the Chern-Simons (CS) field theory 3,4,5,6,7,8,9,10,11,12,13,14,15,16 . Here we present a formulation of the CS theory which resolves several nagging questions and exposes the physics in a particularly transparent way.…”

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confidence: 99%

Towards a Field Theory of Fractional Quantum Hall States

1997

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We present a Chern-Simons theory of the fractional quantum Hall effect in which flux attachment is followed by a transformation that effectively attaches the correlation holes. We extract the correlated wavefunctions, compute the drift and cyclotron currents (due to inhomogeneous density), exhibit the Read operator, and operators that create quasi-particles and holes. We show how the bare kinetic energy can get quenched and replaced by one due to interactions. We find that for ν = 1/2 the low energy theory has neutral quasiparticles and give the effective hamiltonian and constraints.The experimental discovery of the Fractional Quantum Hall Effect 1,2 led to theoretical response on two fronts: trial wavefunctions that captured the essential physics and approximate computational schemes starting with the microscopic hamiltonian. The most successful among the latter has been the Chern-Simons (CS) field theory 3,4,5,6,7,8,9,10,11,12,13,14,15,16 . Here we present a formulation of the CS theory which resolves several nagging questions and exposes the physics in a particularly transparent way. We illustrate our method through the cases ν = 1/3 and ν = 1/2, where the filling fraction ν = 2πn/eB, n being the particle density, −e the electron charge and B the magnetic field down the z-axis. Our results for ν = p/(2np + 1) will be reported later. We set h = c = volume = 1, z = x + iy, and l 0 = (eB) −1/2 the cyclotron length.In the CS approach one introduces a wavefunction for the CS particles in terms of the electronic one as follows:where l is the number of flux quanta to be attached. The prefactor introduces a gauge field a obeyingIn second quantized form, the CS action density iswhere A is the external vector potential and m is the bare mass. The coulomb interaction will be added later. By shifting a we can cancel eA upon choosing l = 3 for ν = 1/3 and l = 2 for ν = 1/2. Hereafter a and ψ † ψ = ρ (the density) will denote normal-ordered quantities. Whereas in the quest for wavefunctions, we can build in not just the phase, but all of (z i − z j ) l , or even the ubiquitous gaussian factors into the process of flux attachment, doing so here would lead to a complex vector potential. 17 . The correlation zeros must therefore be extracted out of the fluctuations 13 . We now introduce our scheme (inspired by the work of Bohm-Pines 18 ) and define a composite particle (CP) field, where P may stand for fermion F or boson B:The transformation kills the a 0 ψψ term and introduces a longitudinal vector potential 2πl P defined byin the kinetic energy term, while a 0 ( ∇×a 2πl ) becomeswhere P = −iq · P and a = iq × a, so that the longitudinal and transverse vector potential are now canonically conjugate and the constraint field has become dynamical! The hamiltonian density is H = 1 2m |(−i∇ + a + 2πlP)ψ| 2= 1 2m |∇ψ| 2 + n 2m (a 2 + 4π 2 l 2 P 2 )

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“…This is guaranteed in the continuum, where Fetter et al did find a gapless collective mode. 19 We have computed the TKKN integer for the triangular and Kagomé lattices using the method of MacDonald 20 and found in both cases ν = −1 = π θ = 1. Hence we expect the Chern-Simons field to be massive and the quantum XY model is therefore likely to have a gap assuming no broken translation symmetry.…”

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confidence: 99%

Possible spin-liquid states on the triangular and kagomé lattices

1993

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The frustrated quantum spin-one-half Heisenberg model on the triangular and Kagomé lattices is mapped onto a single species of fermion carrying statistical flux θ = π. The corresponding Chern-Simons gauge theory is analyzed at the Gaussian level and found to be massive. This provides a new motivation for the spin-liquid Kalmeyer-Laughlin wave function. Good overlap of this wave function with the numerical ground state is found for small clusters.

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Random-phase approximation in the fractional-statistics gas

Cited by 381 publications

References 3 publications

Singular or non-Fermi liquids

Singular or non-Fermi liquids

Towards a Field Theory of Fractional Quantum Hall States

Possible spin-liquid states on the triangular and kagomé lattices

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