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Physical review. B, Condensed matter

Decomposition approach to a two-dimensional electron system with an even-denominator filling factor

Jian Cheng Yang

Published Sep 15, 1994• 2 citations
Publisher

Abstract

A decomposition approach is developed to study a two-dimensional electron system with an even-denominator Landau-level filling factor. This approach divides the electron system into two subsystems---a boson system with bosonic Laughlin ground state and a fermion system with a Fermi surface, interacting with a gauge field. A comparison to the Chern-Simons gauge-field theory is made.

DOI
10.1103/physrevb.50.8028

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A decomposition approach is developed to study a two-dimensional electron system with an even-denominator Landau-level filling factor. This approach divides the electron system into two subsystems---a boson system with bosonic Laughlin ground state and a fermion system with a Fermi surface, interacting with a gauge field. A comparison to the Chern-Simons gauge-field theory is made.
We have previously studied the phase structure at finite temperatures of the Chern-Simons (CS) gauge theory coupled with fermions by using lattice gauge theory. In this paper, we formulate the “chargeon-fluxon ” representation of electrons and use it to reinvestigate the phenomenon of particle-flux separation (PFS) of electrons in the halffilled Landau level. We start with a lattice system of fermions interacting with a CS gauge field, and introduce two slave operators named chargeon and fluxon that carry the CS charge and flux, respectively. The original fermion, the composite fermion of Jain, is a composite of a chargeon and a fluxon. We further rewrite the model by introducing an auxiliary link field, the phase of which behaves as a gauge field gluing chargeons and fluxons. Then we study a confinement-deconfinement transition of that gauge field by using the theory of separation phenomena as in the previous paper. The residual four-fermi interactions play an important role to determine the critical temperature TPFS, below which the PFS takes place. The new representation
A simple one-dimensional model is proposed, in which N spinless repulsively interacting fermions occupy M > N degenerate states. It is argued that the energy spectrum and the wavefunctions of this system strongly resemble the spectrum and wavefunctions of 2D electrons in the lowest Landau level (the problem of the Fractional Quantum Hall Effect). In particular, Laughlin-type wavefunctions describe ground states at filling factors v = N/M = 1/ q , q odd.. Within this model the complimentary wavefunction for v =1−1/ q is found explicitly, and extremely simple ground state wavefunctions for arbitrary odd-denominator filling factors are proposed.
A solvable microscopic model of interacting electrons in a half-filled Landau level is presented. The Hamiltonian is a well-defined limit of the electron-electron interaction. The low energy sector consists of a set of independent, spatially interlaced, one-dimensional systems of non-interacting fermionic dipoles, each system with a Fermi sea ground state. The total number of dipoles in the set of Fermi seas forming the two-dimensional ground state equals the number of electrons in the system and the density of states at the Fermi level is that of a two-dimensional Fermi gas. The model is obtained by generalizing, or rather adopting, the existing exact solution on a thin, but not too thin, torus to the two-dimensional bulk case.
Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question as to whether such an approximation is meaningful arises immediately. We here study 2D interacting electrons in a half-filled Landau level mapped onto interacting hard-core bosons in a magnetic field. We argue that an interacting hard-core boson system in a uniform external field such that there is one flux quantum per particle (unit filling) exhibits an integer quantum Hall effect. As a consequence, the mean-field approximation for mapping electrons at half-filling to a boson system at integer filling fails. \textcopyright{} 1996 The American Physical Society.
We present a many-body approach to calculate the ground-state properties of a system of electrons in a half-filled Landau level. Our starting point is a simplified version of the recently proposed trial wave function where one includes the antisymmetrization operator to the bosonic Laughlin state. Using the classical plasma analogy, we calculate the pair-correlation function, the static structure function, and the ground-state energy in the thermodynamic limit. These results are in good agreement with the expected behavior at $\ensuremath{\nu}=$12\frac{1}{2}21​.