arXiv:cond-mat/9607147

Study of composite fermions: Beyond few particle systems

Jainendra K. Jain, Rajiv K. Kamilla

Published Jul 22, 1996• 0 citations

Abstract

We construct a new representation of composite fermion wave functions in the lowest Landau level which enables Monte Carlo computations at arbitrary filling factors for a fairly large number of composite fermions, thus clearing the way toward a more detailed quantitative investigation of the fractional quantum Hall effect. As an illustrative application, thermodynamic estimates for the transport gaps of several spin polarized incompressible states have been obtained.

DOI: 10.48550/arxiv.cond-mat/9607147

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arXiv:cond-mat/9607147

Study of composite fermions: Beyond few particle systems

Jainendra K. Jain, Rajiv K. Kamilla

Published Jul 22, 1996• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9607147

Related papers

Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level

Jainendra K. Jain, Rajiv K. Kamilla

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States of interacting composite fermions at the Landau level filling ν=2+3/8

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There is increasing experimental evidence for fractional quantum Hall effect at filling factor $\ensuremath{\nu}=2+3/8$. Modeling it as a system of composite fermions, we study the problem of interacting composite fermions by a number of methods. In our variational study, we consider the Fermi sea, the Pfaffian paired state, and bubble and stripe phases of composite fermions, and find that the Fermi sea state is favored for a wide range of transverse thickness. However, when we incorporate interactions between composite fermions through composite-fermion diagonalization on systems with up to 25 composite fermions, we find that a gap opens at the Fermi level, suggesting that inter-composite fermion interaction can induce fractional quantum Hall effect at $\ensuremath{\nu}=2+3/8$. The resulting state is seen to be distinct from the Pfaffian wave function.There is increasing experimental evidence for fractional quantum Hall effect at filling factor $\ensuremath{\nu}=2+3/8$. Modeling it as a system of composite fermions, we study the problem of interacting composite fermions by a number of methods. In our variational study, we consider the Fermi sea, the Pfaffian paired state, and bubble and stripe phases of composite fermions, and find that the Fermi sea state is favored for a wide range of transverse thickness. However, when we incorporate interactions between composite fermions through composite-fermion diagonalization on systems with up to 25 composite fermions, we find that a gap opens at the Fermi level, suggesting that inter-composite fermion interaction can induce fractional quantum Hall effect at $\ensuremath{\nu}=2+3/8$. The resulting state is seen to be distinct from the Pfaffian wave function.

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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 $\ensuremath{\nu}=2/3$,

4/5

, and

3/4

, although it is less satisfactory for the $\ensuremath{\nu}=3/2$ state. For $\ensuremath{\nu}=4/3$ 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 $\ensuremath{\nu}=4/3$ state is more likely to be a spin-singlet state of reverse-flux-attached composite fermions at filling ${\ensuremath{\nu}}^{*}=4$. We also consider incompressible states at integral filling factors $\ensuremath{\nu}=1$ and 2. The incompressible state at $\ensuremath{\nu}=1$ is shown to be well described by the parton-based Jain spin-singlet wave function, and the incompressible state at $\ensuremath{\nu}=2$ as the spin-singlet state of reverse-flux-attached composite fermions at ${\ensuremath{\nu}}^{*}=2$, which provides an example of the bosonic integer topological phase.

1∕3

in the second Landau level (which corresponds to

7∕3

of experiment).

We compare quantum Hall systems at filling factors $\ensuremath{\nu}=2$ to $\ensuremath{\nu}=\frac{2}{3}$ and

\frac{2}{5}

, corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization

P=1

) and paramagnetic

(P=0)

incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the excitation spectra are different. At $\ensuremath{\nu}=2$, we find spin domains at half-polarization

(P=\frac{1}{2})

, while antiferromagnetic order seems most favorable in the CF systems. The transition between

P=0

and 1, as seen when, e.g., the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompressible half-polarized state is found in some models.