Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Springer series in solid-state sciences

Analogy Between Fractional Quantum Hall Effect and Commensurate Flux Phase States on a Lattice

Fedor Vasilievich Kusmartsev

Published Jan 1, 1992• 0 citations
Publisher
DOI
10.1007/978-3-642-84408-9_39

Related papers

The lattice gas model of fractional quantum hall effect

B. Rosenstein, Israel D. Vagner

Physics Letters A•Jul 1, 1986•2 citations

Chiral phase states of the Hubbard Hamiltonian

Fedor Vasilievich Kusmartsev, MANFRED L. RISTIG

We present a variational approach different from that based on Gutzwiller's ansatz by investigating chiral flux-phase states of the Hubbard Hamiltonian in analogy to the treatment of the fractional quantum Hall effect. The proposed class of generalized Laughlin trial functions is specialized to permit detailed consideration of a set of states that includes a ferromagnetic ground state generated by a spontaneous gauge field in conjunction with a fictitious magnetic field having a flux commensurate with the filling. We evaluate the trial energy expectation values and demonstrate that the treatment is, at least, appropriate for the Hubbard model with sufficiently large on-site Coulomb repulsion and low electron densities. The members of the special set of trial states may be suitably classified by the flux quanta of the associated field and may be characterized either by integer or fractional quantum numbers. The excitations designated by fractional quantum numbers, which are not commensurate with the filling, are identified as flux-phase states breaking the symmetries of the lattice.

Physical review. B, Condensed matter•Sep 1, 1991•6 citations

Fractional quantum Hall states in the vicinity of Mott plateaus

R. O. Umucalılar, Erich J. Mueller

We perform variational Monte Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions, and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one another and to the energies found in full configuration-interaction calculations on small systems. We look at overlaps between our variational states and the exact ground state, characterizing the ways in which fractional quantum Hall effect correlations manifest themselves near the Mott insulating state. We explore the experimental signatures of these states.

arXiv:1002.4099•Physical Review A•May 24, 2010•28 citations

Ground State for Fractional Quantum Hall Effect

Ahmed Jellal

International Journal of Theoretical Physics•Feb 1, 2000•0 citations

Equivalence of fractional quantum Hall and resonating-valence-bond states on a square lattice

Z. Zou, Benoît Douçot, B. Sriram Shastry

We show that a fractional quantum Hall state is equivalent to one particular resonating-valence-bond (RVB) state, the ``flux phase'' on a square lattice. The fictitious magnetic flux is dynamically generated in the RVB state. The fractional quantum Hall wave function for the flux phase is explicitly shown to be a singlet.

Physical review. B, Condensed matter•Jun 1, 1989•34 citations

Theory of the Fractional Quantum Hall Effect

Allan H. MacDonald

Recent Progress in Many-Body Theories•Jan 1, 1988•0 citations
We present a variational approach different from that based on Gutzwiller's ansatz by investigating chiral flux-phase states of the Hubbard Hamiltonian in analogy to the treatment of the fractional quantum Hall effect. The proposed class of generalized Laughlin trial functions is specialized to permit detailed consideration of a set of states that includes a ferromagnetic ground state generated by a spontaneous gauge field in conjunction with a fictitious magnetic field having a flux commensurate with the filling. We evaluate the trial energy expectation values and demonstrate that the treatment is, at least, appropriate for the Hubbard model with sufficiently large on-site Coulomb repulsion and low electron densities. The members of the special set of trial states may be suitably classified by the flux quanta of the associated field and may be characterized either by integer or fractional quantum numbers. The excitations designated by fractional quantum numbers, which are not commensurate with the filling, are identified as flux-phase states breaking the symmetries of the lattice.
We perform variational Monte Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions, and the deviation of density from an integer is commensurate with the effective magnetic field. We compare the energies of superfluid and correlated states to one another and to the energies found in full configuration-interaction calculations on small systems. We look at overlaps between our variational states and the exact ground state, characterizing the ways in which fractional quantum Hall effect correlations manifest themselves near the Mott insulating state. We explore the experimental signatures of these states.