173 research outputs found
Generalized Quantum Hall Projection Hamiltonians
Certain well known quantum Hall states -- including the Laughlin states, the
Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined
as the unique lowest degree symmetric analytic function that vanishes as at
least p powers as some number (g+1) of particles approach the same point.
Analogously, these same quantum Hall states can be generated as the exact
highest density zero energy state of simple angular momentum projection
operators. Following this theme we determine the highest density zero energy
state for many other values of p and g.Comment: 9 page
Universality of the edge tunneling exponent of fractional quantum Hall liquids
Recent calculations of the edge tunneling exponents in quantum Hall states
appear to contradict their topological nature. We revisit this issue and find
no fundamental discrepancies. In a microscopic model of fractional quantum Hall
liquids with electron-electron interaction and confinement, we calculate the
edge Green's function via exact diagonalization. Our results for
and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of
the edge and the strength of the edge confining potential, which can lead to
edge reconstruction, are the parameters that are relevant to the universality
of the electron tunneling I-V exponent.Comment: 5 pages, 3 figure
Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
We study the ground state and low-energy excitations of fractional quantum
Hall systems on a disk at filling fraction , with Coulomb
interaction and background confining potential. We find the Moore-Read ground
state is stable within a finite but narrow window in parameter space. The
corresponding low-energy excitations contain a fermionic branch and a bosonic
branch, with widely different velocities. A short-range repulsive potential can
stabilize a charge quasihole at the center, leading to a different edge
excitation spectrum due to the change of boundary conditions for Majorana
fermions, clearly indicating the non-Abelian nature of the quasihole.Comment: 4 pages, 3 figures. New version shortened for PRL. Corrected typo
Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level
We present results of extensive numerical calculations on the ground state of
electrons in the first excited (n=1) Landau level with Coulomb interactions,
and including non-zero thickness effects, for filling factors 12/5 and 13/5 in
the torus geometry. In a region that includes these experimentally-relevant
values, we find that the energy spectrum and the overlaps with the trial states
support the previous hypothesis that the system is in the non-Abelian k = 3
liquid phase we introduced in a previous paper.Comment: 5 pages (Revtex4), 7 figure
Coulomb and Hard Core Skyrmion Tails
Quantum Hall skyrmions are quantized solitons of a ferromagnetic O(3)
sigma-model. The reference, classical, solutions depend upon the interaction
between the electrons and exhibit completely different asymptotic profiles for
the physical Coulomb interaction than for the model hard core interaction
frequently used to generate variational wavefunctions. In this note we show, by
means of numerical calculations on (large) finite size systems at nu=1, that
this physically important difference, crucial for a sharp definition of their
statistics, persists for the quantized skyrmions at n=1.Comment: Revtex 9 pages, figs.ps files at
ftp://landau.calstatela.edu/pub/tailfig
A nu=2/5 Paired Wavefunction
We construct a wavefunction, generalizing the well known Moore-Read Pfaffian,
that describes spinless electrons at filling fraction nu=2/5 (or bosons at
filling fraction nu=2/3) as the ground state of a very simple three body
potential. We find, analogous to the Pfaffian, that when quasiholes are added
there is a ground state degeneracy which can be identified as zero-modes of the
quasiholes. The zero-modes are identified as having semionic statistics. We
write this wavefunction as a correlator of the Virasoro minimal model conformal
field theory M(5,3). Since this model is non-unitary, we conclude that this
wavefunction is a quantum critical state. Nonetheless, we find that the
overlaps of this wavefunction with exact diagonalizations in the lowest and
first excited Landau level are very high, suggesting that this wavefunction may
have experimental relevance for some transition that may occur in that regime.Comment: 13 pages, 2 figure
Low ordered magnetic moment by off-diagonal frustration in undoped parent compounds to iron-based high-Tc superconductors
A Heisenberg model over the square lattice recently introduced by Si and
Abrahams to describe local-moment magnetism in the new class of Fe-As high-Tc
superconductors is analyzed in the classical limit and on a small cluster by
exact diagonalization. In the case of spin-1 iron atoms, large enough
Heisenberg exchange interactions between neighboring spin-1/2 moments on
different iron 3d orbitals that frustrate true magnetic order lead to hidden
magnetic order that violates Hund's rule. It accounts for the low ordered
magnetic moment observed by elastic neutron diffraction in an undoped parent
compound to Fe-As superconductors. We predict that low-energy spin-wave
excitations exist at wavenumbers corresponding to either hidden Neel or hidden
ferromagnetic order.Comment: 7 pages, 6 figures, version published in Physical Review Letter
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