15 research outputs found
Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
We perform numerical studies to determine if the fractional quantum Hall
state observed at filling nu=5/2 is the Moore-Read wavefunction or its particle
hole conjugate, the so-called AntiPfaffian. Using a truncated Hilbert space
approach we find that for realistic interactions, including Landau-level
mixing, the ground state remains fully polarized and the AntiPfaffian is
strongly favored.Comment: Main change is that the Anti-Pfaffian is favored instead of the
Pfaffian (caused by a sign error in the commutation relation of the dynamical
momenta). 4-plus pages, 3 figure
Landau Level Mixing in the Perturbative Limit
We study the effects of Landau level mixing in the limit of weak electron
interaction. We use a numerical method to obtain the two- and three-body
corrections to quantum Hall pseudopotentials, which are exact to lowest order
in the Landau level mixing parameter. Our results are in general agreement with
certain analytic results (some derived here, some derived by other authors) in
the thermodynamic limit. We find that the convergence to this thermodynamic
limit can be slow. This suggests that errors could occur if one tries to use
pseudopotentials derived in a thermodynamic limit for numerical work on finite
systems.Comment: 6 pages; published version Phys. Rev. B 87, 155426; Published 22
April 201
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
Paired composite fermion phase of quantum Hall bilayers at \nu = 1/2 + 1/2
We provide numerical evidence for composite fermion pairing in quantum Hall
bilayer systems at filling for intermediate spacing between the
layers. We identify the phase as pairing, and construct high
accuracy trial wavefunctions to describe the groundstate on the sphere. For
large distances between the layers, and for finite systems, a competing "Hund's
rule" state, or composite fermion liquid, prevails for certain system sizes. We
argue that for larger systems, the pairing phase will persist to larger layer
spacing.Comment: 4 pages, 2 figures; v2: final version, as published in journa
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
Entanglement entropy of the composite fermion non-Fermi liquid state
The so-called ``non-Fermi liquid'' behavior is very common in strongly
correlated systems. However, its operational definition in terms of ``what it
is not'' is a major obstacle against theoretical understanding of this
fascinating correlated state. Recently there has been much interest in
entanglement entropy as a theoretical tool to study non-Fermi liquids. So far
explicit calculations have been limited to models without direct experimental
realizations. Here we focus on a two dimensional electron fluid under magnetic
field and filling fraction , which is believed to be a non-Fermi
liquid state. Using the composite fermion (CF) wave-function which captures the
state very accurately, we compute the second R\'enyi entropy using
variational Monte-Carlo technique and an efficient parallel algorithm. We find
the entanglement entropy scales as with the length of the boundary
as it does for free fermions, albeit with a pre-factor twice that of the
free fermion. We contrast the results against theoretical conjectures and
discuss the implications of the results.Comment: 4+ page
Evidence for a topological "exciton Fermi sea" in bilayer graphene
The quantum Hall physics of bilayer graphene is extremely rich due to the interplay between a layer degree of freedom and delicate fractional states. Recent experiments show that when an electric field perpendicular to the bilayer causes Landau levels of opposing layers to cross in energy, a even-denominator Hall plateau can coexist with a finite density of inter-layer excitons. We present theoretical and numerical evidence that this observation is due to a new phase of matter - a Fermi sea of topological excitons
Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude
We study the scaling behavior in the tunneling amplitude when quasiparticles
tunnel along a straight path between the two edges of a fractional quantum Hall
annulus. Such scaling behavior originates from the propagation and tunneling of
charged quasielectrons and quasiholes in an effective field analysis. In the
limit when the annulus deforms continuously into a quasi-one-dimensional ring,
we conjecture the exact functional form of the tunneling amplitude for several
cases, which reproduces the numerical results in finite systems exactly. The
results for Abelian quasiparticle tunneling is consistent with the scaling
anaysis; this allows for the extraction of the conformal dimensions of the
quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian
quasiparticles in the Read-Rezayi Z_k-parafermion states. Interestingly, the
non-Abelian quasiparticle tunneling amplitudes exhibit nontrivial k-dependent
corrections to the scaling exponent.Comment: 16 pages, 4 figure
Trial wave functions for ?=(1)/(2)+(1)/(2) quantum Hall bilayers
Quantum Hall bilayer systems at filling fractions near \nu=\half+\half undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation is reduced below some critical value. Deep in the intralayer phase (large separation) the system can be interpreted as a fluid of composite fermions (CFs), whereas deep in the interlayer phase (small separation) the system can be interpreted as a fluid of composite bosons (CBs). The focus of this paper is to understand the states that occur for intermediate layer separation by using variational wavefunctions. We consider two main classes of wavefunctions. In the first class, first discussed by PRL {\bf 77}, 3009 (1996), we consider interlayer BCS pairing of two independent CF liquids. We find that these wavefunctions are exceedingly good for with the magnetic length. The second class of wavefunctions naturally follows the reasoning of PRL {\bf 91}, 046803 (2003) and generalizes the idea of pairing wavefunctions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wavefunctions for interlayer spacings of , as well. The accuracy of the wavefunctions discussed in this work, compared with exact diagonalization, is comparable to that of the celebrated Laughlin wavefunction. We conclude that over a range of there exists a phase of interlayer BCS-paired composite fermions. At smaller , we find a second order transition to a composite boson liquid, known also as the 111 phase