Composite fermions on a torus

Songyang Pu, Ying Hai Wu, J. K. Jain

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We achieve an explicit construction of the lowest Landau level (LLL) projected wave functions for composite fermions in the periodic (torus) geometry. To this end, we first demonstrate how the vortex attachment of the composite fermion (CF) theory can be accomplished in the torus geometry to produce the "unprojected" wave functions satisfying the correct (quasi)periodic boundary conditions. We then consider two methods for projecting these wave functions into the LLL. The direct projection produces valid wave functions but can be implemented only for very small systems. The more powerful and more useful projection method of Jain and Kamilla fails in the torus geometry because it does not preserve the periodic boundary conditions and thus takes us out of the original Hilbert space. We have succeeded in constructing a modified projection method that is consistent with both the periodic boundary conditions and the general structure of the CF theory. This method is valid for a large class of states of composite fermions, called "proper states," which includes the incompressible ground states at electron filling factors ν=n2pn+1, their charged and neutral excitations, and also the quasidegenerate ground states at arbitrary filling factors of the form ν=ν∗2pν∗+1, where n and p are integers and ν∗ is the CF filling factor. Comparison with exact results known for small systems for the ground and excited states at filling factors ν=1/3, 2/5, and 3/7 demonstrates our LLL-projected wave functions to be extremely accurate representations of the actual Coulomb eigenstates. Our construction enables the study of large systems of composite fermions on the torus, thereby opening the possibility of investigating numerous interesting questions and phenomena.

Original languageEnglish (US)
Article number195302
JournalPhysical Review B
Volume96
Issue number19
DOIs
StatePublished - Nov 7 2017

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Fermions
Wave functions
fermions
wave functions
composite materials
Composite materials
Ground state
projection
Boundary conditions
boundary conditions
ground state
Geometry
geometry
Hilbert spaces
Hilbert space
Excited states
excitation
integers
attachment
eigenvectors

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Pu, Songyang ; Wu, Ying Hai ; Jain, J. K. / Composite fermions on a torus. In: Physical Review B. 2017 ; Vol. 96, No. 19.
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Composite fermions on a torus. / Pu, Songyang; Wu, Ying Hai; Jain, J. K.

In: Physical Review B, Vol. 96, No. 19, 195302, 07.11.2017.

Research output: Contribution to journalArticle

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