44 research outputs found
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
Incompressible liquid state of rapidly-rotating bosons at filling factor 3/2
Bosons in the lowest Landau level, such as rapidly-rotating cold trapped
atoms, are investigated numerically in the specially interesting case in which
the filling factor (ratio of particle number to vortex number) is 3/2. When a
moderate amount of a longer-range (e.g. dipolar) interaction is included, we
find clear evidence that the ground state is in a phase constructed earlier by
two of us, in which excitations possess non-Abelian statistics.Comment: 5 pages, 5 figure
Real-space entanglement spectrum of quantum Hall systems
We study the real-space entanglement spectrum for fractional quantum Hall
systems, which maintains locality along the spatial cut, and provide evidence
that it possesses a scaling property. We also consider the closely-related
particle entanglement spectrum, and carry out the Schmidt decomposition of the
Laughlin state analytically at large size.Comment: 5 pages, 4 figures. V2: a bit more on non-locality of OP. V3: typos
corrected; as publishe
Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
The quasihole states of several paired states, the Pfaffian, Haldane-Rezayi,
and 331 states, which under certain conditions may describe electrons at
filling factor or 5/2, are studied, analytically and numerically, in
the spherical geometry, for the Hamiltonians for which the ground states are
known exactly. We also find all the ground states (without quasiparticles) of
these systems in the toroidal geometry. In each case, a complete set of
linearly-independent functions that are energy eigenstates of zero energy is
found explicitly. For fixed positions of the quasiholes, the number of
linearly-independent states is for the Pfaffian, for the
Haldane-Rezayi state; these degeneracies are needed if these systems are to
possess nonabelian statistics, and they agree with predictions based on
conformal field theory. The dimensions of the spaces of states for each number
of quasiholes agree with numerical results for moderate system sizes. The
effects of tunneling and of the Zeeman term are discussed for the 331 and
Haldane-Rezayi states, as well as the relation to Laughlin states of electron
pairs. A model introduced by Ho, which was supposed to connect the 331 and
Pfaffian states, is found to have the same degeneracies of zero-energy states
as the 331 state, except at its Pfaffian point where it is much more highly
degenerate than either the 331 or the Pfaffian. We introduce a modification of
the model which has the degeneracies of the 331 state everywhere including the
Pfaffian point; at the latter point, tunneling reduces the degeneracies to
those of the Pfaffian state. An experimental difference is pointed out between
the Laughlin states of electron pairs and the other paired states, in the
current-voltage response when electrons tunnel into the edge. And there's more.Comment: 43 pages, requires RevTeX. The 14 figures and 2 tables are available
on request at [email protected] (include mailing address
SU(N) Quantum Hall Skyrmions
We have investigated skyrmions in N-component quantum Hall systems. We find
that SU(N) skyrmions are the lowest energy charged excitations for filling
factors \nu = 1,2,...,N-1 for small enough symmetry breaking terms. N>2
skyrmions can be realized in Si QH systems based on the (110) or (111)
interfaces of Si, or perhaps in Si (100) systems, where the spin and valley
isospin together provide an SU(4)-symmetry, or in multilayer QH systems. We
also present Hartree-Fock results for a phenomenological easy-axis
SU(2)-breaking model appropriate to valley degeneracy.Comment: 5 pages, 2 figure
Field theory of spin-singlet quantum Hall states
We formulate a field theory for a class of spin-singlet quantum Hall states
(the Haldane-Rezayi state and its variants) which have been proposed for the
quantized Hall plateaus observed at the second lowest Landau level. A new
essential ingredient is a class of super Chern-Simons field. We show that the
known properties of the states are consistently described by it. We also give a
2+1 dimensional hierarchical construction. Implications of the proposal are
discussed and a new physical picture of composite particles at the second
lowest Landau level emerges.Comment: RevTex, 5 pages, 1 figur
Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
The Hall viscosity, a non-dissipative transport coefficient analogous to Hall
conductivity, is considered for quantum fluids in gapped or topological phases.
The relation to mean orbital spin per particle discovered in previous work by
one of us is elucidated with the help of examples, using the geometry of shear
transformations and rotations. For non-interacting particles in a magnetic
field, there are several ways to derive the result (even at non-zero
temperature), including standard linear response theory. Arguments for the
quantization, and the robustness of Hall viscosity to small changes in the
Hamiltonian that preserve rotational invariance, are given. Numerical
calculations of adiabatic transport are performed to check the predictions for
quantum Hall systems, with excellent agreement for trial states. The
coefficient of k^4 in the static structure factor is also considered, and shown
to be exactly related to the orbital spin and robust to perturbations in
rotation invariant systems also.Comment: v2: Now 30 pages, 10 figures; new calculation using disk geometry;
some other improvements; no change in result
Bulk and edge correlations in the compressible half-filled quantum Hall state
We study bulk and edge correlations in the compressible half-filled state,
using a modified version of the plasma analogy. The corresponding plasma has
anomalously weak screening properties, and as a consequence we find that the
correlations along the edge do not decay algebraically as in the Laughlin
(incompressible) case, while the bulk correlations decay in the same way. The
results suggest that due to the strong coupling between charged modes on the
edge and the neutral Fermions in the bulk, reflected by the weak screening in
the plasma analogue, the (attractive) correlation hole is not well defined on
the edge. Hence, the system there can be modeled as a free Fermi gas of {\em
electrons} (with an appropriate boundary condition). We finally comment on a
possible scenario, in which the Laughlin-like dynamical edge correlations may
nevertheless be realized.Comment: package now includes the file epsfig.sty, needed to incorporate
properly the 8 magnificent figure
Separation of spin and charge in paired spin-singlet quantum Hall states
We propose a series of paired spin-singlet quantum Hall states, which exhibit
a separation of spin and charge degrees of freedom. The fundamental excitations
over these states, which have filling fraction \nu=2/(2m+1) with m an odd
integer, are spinons (spin-1/2 and charge zero) or fractional holons (charge
+/- 1/(2m+1) and spin zero). The braid statistics of these excitations are
non-abelian. The mechanism for the separation of spin and charge in these
states is topological: spin and charge excitations are liberated by binding to
a vortex in a p-wave pairing condensate. We briefly discuss related, abelian
spin-singlet states and possible transitions.Comment: 4 pages, uses revtex
Edge of a Half-Filled Landau Level
We have investigated the electron occupation number of the edge of a quantum
Hall (QH) droplet at using exact diagonalization technique and
composite fermion trial wavefunction. We find that the electron occupation
numbers near the edge obey a scaling behavior. The scaling result indicates the
existence of a well-defined edge corresponding to the radius of a compact
droplet of uniform filling factor 1/2. We find that the occupation number
beyond this edge point is substantial, which is qualitatively different from
the case of odd-denominator QH states. We relate these features to the
different ways in which composite fermions occupy Landau levels for odd and
even denominator states.Comment: To appear in Phys. Rev.