18 research outputs found
The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold
degeneracy is realized by two inequivalent crystalline states with a four- and
two-fold degeneracy respectively. The fundamental quasihole and quasiparticle
excitations are domain walls between these vacua, and simple counting arguments
give a Hilbert space of dimension for holes and particles
at fixed positions and assign each a charge . This generalizes the
known properties of the hole excitations in the Pfaffian state as deduced using
conformal field theory techniques. Numerical calculations using a model
hamiltonian and a small number of particles supports the presence of a stable
phase with degenerate vacua and quarter charged domain walls also away from the
thin torus limit. A spin chain hamiltonian encodes the degenerate vacua and the
various domain walls.Comment: 4 pages, 1 figure. Published, minor change
Pedestrian index theorem a la Aharonov-Casher for bulk threshold modes in corrugated multilayer graphene
Zero-modes, their topological degeneracy and relation to index theorems have
attracted attention in the study of single- and bilayer graphene. For
negligible scalar potentials, index theorems explain why the degeneracy of the
zero-energy Landau level of a Dirac hamiltonian is not lifted by gauge field
disorder, for example due to ripples, whereas other Landau levels become
broadened by the inhomogenous effective magnetic field. That also the bilayer
hamiltonian supports such protected bulk zero-modes was proved formally by
Katsnelson and Prokhorova to hold on a compact manifold by using the
Atiyah-Singer index theorem. Here we complement and generalize this result in a
pedestrian way by pointing out that the simple argument by Aharonov and Casher
for degenerate zero-modes of a Dirac hamiltonian in the infinite plane extends
naturally to the multilayer case. The degeneracy remains, though at nonzero
energy, also in the presence of a gap. These threshold modes make the spectrum
asymmetric. The rest of the spectrum, however, remains symmetric even in
arbitrary gauge fields, a fact related to supersymmetry. Possible benefits of
this connection are discussed.Comment: 6 pages, 2 figures. The second version states now also in words that
the conjugation symmetry that in the massive case gets replaced by
supersymmetry is the chiral symmetry. Changes in figure
Quantum corrections in the Boltzmann conductivity of graphene and their sensitivity to the choice of formalism
Semiclassical spin-coherent kinetic equations can be derived from quantum
theory with many different approaches (Liouville equation based approaches,
nonequilibrium Green's functions techniques, etc.). The collision integrals
turn out to be formally different, but coincide in textbook examples as well as
for systems where the spin-orbit coupling is only a small part of the kinetic
energy like in related studies on the spin Hall effect. In Dirac cone physics
(graphene, surface states of topological insulators like Bi_{1-x}Sb_x, Bi_2Te_3
etc.), where this coupling constitutes the entire kinetic energy, the
difference manifests itself in the precise value of the electron-hole coherence
originated quantum correction to the Drude conductivity . The leading correction is derived analytically for single and multilayer
graphene with general scalar impurities. The often neglected principal value
terms in the collision integral are important. Neglecting them yields a leading
correction of order , whereas including them can give a
correction of order . The latter opens up a counterintuitive
scenario with finite electron-hole coherent effects at Fermi energies
arbitrarily far above the neutrality point regime, for example in the form of a
shift that only depends on the dielectric constant. This residual
conductivity, possibly related to the one observed in recent experiments,
depends crucially on the approach and could offer a setting for experimentally
singling out one of the candidates. Concerning the different formalisms we
notice that the discrepancy between a density matrix approach and a Green's
function approach is removed if the Generalized Kadanoff-Baym Ansatz in the
latter is replaced by an anti-ordered version.Comment: 31 pages, 1 figure. An important sign error has been rectified in the
principal value terms in equation (52) in the vN & NSO expression. It has no
implications for the results on the leading quantum correction studied in
this paper. However, for the higher quantum corrections studied in
arXiv:1304.3929 (see comment in the latter) the implications are crucia
Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
We study the collective states of interacting non-Abelian anyons that emerge
in Kitaev's honeycomb lattice model. Vortex-vortex interactions are shown to
lead to the lifting of the topological degeneracy and the energy is discovered
to exhibit oscillations that are consistent with Majorana fermions being
localized at vortex cores. We show how to construct states corresponding to the
fusion channel degrees of freedom and obtain the energy gaps characterizing the
stability of the topological low energy spectrum. To study the collective
behavior of many vortices, we introduce an effective lattice model of Majorana
fermions. We find necessary conditions for it to approximate the spectrum of
the honeycomb lattice model and show that bi-partite interactions are
responsible for the degeneracy lifting also in many vortex systems.Comment: 22 pages, 12 figures, published versio
Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations
We present a microscopic derivation of the generalized Boltzmann and
Eilenberger equations in the presence of non-Abelian gauges, for the case of a
non-relativistic disordered Fermi gas. A unified and symmetric treatment of the
charge and spin degrees of freedom is achieved. Within this
framework, just as the Lorentz force generates the Hall effect, so does
its counterpart give rise to the spin Hall effect. Considering elastic
and spin-independent disorder we obtain diffusion equations for charge and spin
densities and show how the interplay between an in-plane magnetic field and a
time dependent Rashba term generates in-plane charge currents.Comment: 11 pages, 1 figure; some corrections and updated/extended reference
Bose-Einstein condensates in strong electric fields -- effective gauge potentials and rotating states
Magnetically-trapped atoms in Bose-Einstein condensates are spin polarized.
Since the magnetic field is inhomogeneous, the atoms aquire Berry phases of the
Aharonov-Bohm type during adiabatic motion. In the presence of an eletric field
there is an additional Aharonov-Casher effect. Taking into account the
limitations on the strength of the electric fields due to the polarizability of
the atoms, we investigate the extent to which these effects can be used to
induce rotation in a Bose-Einstein condensate.Comment: 5 pages, 2 ps figures, RevTe
Charge and Current in the Quantum Hall Matrix Model
We extend the quantum Hall matrix model to include couplings to external
electric and magnetic fields. The associated current suffers from matrix
ordering ambiguities even at the classical level. We calculate the linear
response at low momenta -- this is unambigously defined. In particular, we
obtain the correct fractional quantum Hall conductivity, and the expected
density modulations in response to a weak and slowly varying magnetic field.
These results show that the classical quantum Hall matrix models describe
important aspects of the dynamics of electrons in the lowest Landau level. In
the quantum theory the ordering ambiguities are more severe; we discuss
possible strategies, but we have not been able to construct a good density
operator, satisfying the pertinent lowest Landau level commutator algebra.Comment: 12 pages, no figures; a logical error below the proposed density
operator (46) in version 1 is corrected, and the claim that this density
operator satisfy the magnetic algebra (2) is withdrawn. Some formulations
have been changed and a few misprints correcte
Solitons and Quasielectrons in the Quantum Hall Matrix Model
We show how to incorporate fractionally charged quasielectrons in the finite
quantum Hall matrix model.The quasielectrons emerge as combinations of BPS
solitons and quasiholes in a finite matrix version of the noncommutative
theory coupled to a noncommutative Chern-Simons gauge field. We also
discuss how to properly define the charge density in the classical matrix
model, and calculate density profiles for droplets, quasiholes and
quasielectrons.Comment: 15 pages, 9 figure
Kaleidoscope of topological phases with multiple Majorana species
Exactly solvable lattice models for spins and non-interacting fermions
provide fascinating examples of topological phases, some of them exhibiting the
localized Majorana fermions that feature in proposals for topological quantum
computing. The Chern invariant is one important characterization of such
phases. Here we look at the square-octagon variant of Kitaev's honeycomb model.
It maps to spinful paired fermions and enjoys a rich phase diagram featuring
distinct abelian and nonabelian phases with and . The and phases all support localized Majorana
modes and are examples of Ising and anyon theories respectively.Comment: 6 pages, 5 figures. The second version has a new title, reflecting a
change of focus of the presentation in this version. The third version
contains minor changes and is essentially the one published in New Journal of
Physic
Matrix Model Description of Laughlin Hall States
We analyze Susskind's proposal of applying the non-commutative Chern-Simons
theory to the quantum Hall effect. We study the corresponding regularized
matrix Chern-Simons theory introduced by Polychronakos. We use holomorphic
quantization and perform a change of matrix variables that solves the Gauss law
constraint. The remaining physical degrees of freedom are the complex
eigenvalues that can be interpreted as the coordinates of electrons in the
lowest Landau level with Laughlin's wave function. At the same time, a
statistical interaction is generated among the electrons that is necessary to
stabilize the ground state. The stability conditions can be expressed as the
highest-weight conditions for the representations of the W-infinity algebra in
the matrix theory. This symmetry provides a coordinate-independent
characterization of the incompressible quantum Hall states.Comment: 31 pages, large additions on the path integral and overlaps, and on
the W-infinity symmetr