188 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
Infinite density matrix renormalization group for multicomponent quantum Hall systems
While the simplest quantum Hall plateaus, such as the state in
GaAs, can be conveniently analyzed by assuming only a single active Landau
level participates, for many phases the spin, valley, bilayer, subband, or
higher Landau level indices play an important role. These `multi-component'
problems are difficult to study using exact diagonalization because each
component increases the difficulty exponentially. An important example is the
plateau at , where scattering into higher Landau levels chooses
between the competing non-Abelian Pfaffian and anti-Pfaffian states. We address
the methodological issues required to apply the infinite density matrix
renormalization group to quantum Hall systems with multiple components and
long-range Coulomb interactions, greatly extending accessible system sizes. As
an initial application we study the problem of Landau level mixing in the state. Within the approach to Landau level mixing used here, we find
that at the Coulomb point the anti-Pfaffian is preferred over the Pfaffian
state over a range of Landau level mixing up to the experimentally relevant
values.Comment: 12 pages, 9 figures. v2 added more data for different amounts of
Landau level mixing at 5/2 fillin
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
Skyrmions in Higher Landau Levels
We calculate the energies of quasiparticles with large numbers of reversed
spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than
or equals 1. We find, in contrast with the known result for filling factor
equals 1 (k = 0), that these quasiparticles always have higher energy than the
fully polarized ones and hence are not the low energy charged excitations, even
at small Zeeman energies. It follows that skyrmions are the relevant
quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe
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
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
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
Quantum Monte-Carlo method without negative-sign problem for two-dimensional electron systems under strong magnetic fields
The quantum Monte-Carlo method is applied to two-dimensional electron systems
under strong magnetic fields. The negative-sign problem involved by this method
can be avoided for certain filling factors by modifying interaction parameters
from those of the Coulomb interaction. Our techniques for obtaining
sign-problem-free parameters are described in detail. Calculated results on
static observables are also reported for Landau level filling .Comment: 4 pages, 3 figure
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
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