223 research outputs found
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
Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
We develop the Density Matrix Renormalization Group (DMRG) technique for
numerically studying incompressible fractional quantum Hall (FQH) states on the
sphere. We calculate accurate estimates for ground state energies and
excitationgaps at FQH filling fractions \nu=1/3 and \nu=5/2 for systems that
are almost twice as large as the largest ever studied by exact diagonalization.
We establish, by carefully comparing with existing numerical results on smaller
systems, that DMRG is a highly effective numerical tool for studying
incompressible FQH states.Comment: 5 pages, 4 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
S3 Quantum Hall Wavefunctions
We construct a family of quantum Hall Hamiltonians whose ground states, at
least for small system sizes, give correlators of the S3 conformal field
theories. The ground states are considered as trial wavefunctions for quantum
Hall effect of bosons at filling fraction nu=3/4 interacting either via delta
function interaction or delta function plus dipole interaction. While the S3
theories can be either unitary or nonunitary, we find high overlaps with exact
diagonalizations only for the nonunitary case, suggesting that these
wavefunctions may correspond to critical points, possibly analogous to the
previously studied Gaffnian wavefunction. These wavefunctions give an explicit
example which cannot be fully characterized by their thin-torus limit or by
their pattern of zeros.Comment: 4+epsilon pages. 1 figure. Revised version includes: 1 additional
author; additional numerical work; several minor corrections. Our main
results are unchange
A Typology for Quantum Hall Liquids
There is a close analogy between the response of a quantum Hall liquid (QHL)
to a small change in the electron density and the response of a superconductor
to an externally applied magnetic flux - an analogy which is made concrete in
the Chern-Simons Landau-Ginzburg (CSLG) formulation of the problem. As the
Types of superconductor are distinguished by this response, so too for QHLs: a
typology can be introduced which is, however, richer than that in
superconductors owing to the lack of any time-reversal symmetry relating
positive and negative fluxes. At the boundary between Type I and Type II
behavior, the CSLG action has a "Bogomol'nyi point," where the quasi-holes
(vortices) are non-interacting - at the microscopic level, this corresponds to
the behavior of systems governed by a set of model Hamiltonians which have been
constructed to render exact a large class of QHL wavefunctions. All Types of
QHLs are capable of giving rise to quantized Hall plateaux.Comment: 4 +epsilon pages, 1 figure; v2 has added references and minor
changes, version published in Phys. Rev. B. (Rapid Communications
Spin polarization of the quantum Hall state
We report on results of numerical studies of the spin polarization of the
half filled second Landau level, which corresponds to the fractional quantum
Hall state at filling factor . Our studies are performed using both
exact diagonalization and Density Matrix Renormalization Group (DMRG) on the
sphere. We find that for the Coulomb interaction the exact finite-system ground
state is fully polarized, for shifts corresponding to both the Moore-Read
Pfaffian state and its particle-hole conjugate (anti-Pfaffian). This result is
found to be robust against small variations of the interaction. The low-energy
excitation spectrum is consistent with spin-wave excitations of a
fully-magnetized ferromagnet.Comment: Final version published on PR
Reconstruction of the Quantum Hall Edge
The sharp \nu=1 quantum Hall edge present for hard confinement is shown to
have two modes that go soft as the confining potential softens. This signals a
second order transition to a reconstructed edge that is either a depolarized
spin-texture edge or a polarized charge density wave edge.Comment: 6 pages, 4 figures, to be published in the proceedings of the
workshop on ``Novel Physics in Low-Dimensional Electron Systems'' held in
Dresden, Physica
Vortex Lattices in Rotating Atomic Bose Gases with Dipolar Interactions
We show that dipolar interactions have dramatic effects on the groundstates
of rotating atomic Bose gases in the weak interaction limit. With increasing
dipolar interaction (relative to the net contact interaction), the mean-field,
or high filling fraction, groundstate undergoes a series of transitions between
vortex lattices of different symmetries: triangular, square, ``stripe'', and
``bubble'' phases. We also study the effects of dipolar interactions on the
quantum fluids at low filling fractions. We show that the incompressible
Laughlin state at filling fraction is replaced by compressible stripe
and bubble phases.Comment: 4 pages, 2 figure
Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge
We give a microscopic derivation of the chiral Luttinger liquid theory for
the Laughlin states. Starting from the wave function describing an arbitrary
incompressibly deformed Laughlin state (IDLS) we quantize these deformations.
In this way we obtain the low-energy projections of local microscopic operators
and derive the quantum field theory of edge excitations directly from quantum
mechanics of electrons. This shows that to describe experimental and numeric
deviations from chiral Luttinger liquid theory one needs to go beyond
Laughlin's approximation. We show that in the large N limit the IDLS is
described by the dispersionless Toda hierarchy.Comment: 5 pages, revtex, several clarifying comments adde
- …