186 research outputs found
Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
Particles obeying non-Abelian braid statistics have been predicted to emerge
in the fractional quantum Hall effect. In particular, a model Hamiltonian with
short-range three-body interaction () between electrons
confined to the lowest Landau level provides exact solutions for quasiholes,
and thereby allows a proof of principle for the existence of quasiholes obeying
non-Abelian braid statistics. We construct, in terms of two- and three- body
Haldane pseudopotentials, a model Hamiltonian that can be solved exactly for
both quasiholes and quasiparticles, and provide evidence of non-Abelian
statistics for the latter as well. The structure of the quasiparticle states of
this model is in agreement with that predicted by the bipartite
composite-fermion model of quasiparticles with exact lowest Landau level
projection. We further demonstrate adiabatic continuity for the ground state,
the ordinary neutral excitation, and the topological exciton as we deform our
model Hamiltonian continuously into the lowest Landau-level
Hamiltonian.Comment: 15 pages, 10 figure
Candidate local parent Hamiltonian for 3/7 fractional quantum Hall effect
While a parent Hamiltonian for Laughlin wave function has been long
known in terms of the Haldane pseudopotentials, no parent Hamiltonians are
known for the lowest-Landau-level projected wave functions of the composite
fermion theory at with . If one takes the two lowest Landau
levels to be degenerate, the Trugman-Kivelson interaction produces the
unprojected 2/5 wave function as the unique zero energy solution. If the lowest
three Landau levels are assumed to be degenerate, the Trugman-Kivelson
interaction produces a large number of zero energy states at . We
propose that adding an appropriately constructed three-body interaction yields
the unprojected wave function as the unique zero energy solution, and
report extensive exact diagonalization studies that provide strong support to
this proposal.Comment: 11 pages, 2 figure
Real-space entanglement spectra of parton states in fractional quantum Hall systems
Real-space entanglement spectra (RSES) capture characteristic features of the
topological order encoded in the fractional quantum Hall (FQH) states. In this
work, we numerically compute, using Monte Carlo methods, the RSES and the
counting of edge excitations of non-Abelian FQH states constructed using the
parton theory. Efficient numerical computation of RSES of parton states is
possible, thanks to their product-of-Slater-determinant structure, allowing us
to compute the spectra in systems of up to 80 particles. Specifically, we
compute the RSES of the parton states , , and ,
where is the wave function of filled Landau levels, in the ground
state as well as in the presence of bulk quasihole states. We then explicitly
demonstrate a one-to-one correspondence of RSES of the parton states with
representations of the Kac-Moody algebras satisfied by their edge currents. We
also show that for the lowest Landau level projected version of these parton
states, the spectra match with that obtained from the edge current algebra. We
also perform a computation of spectra of the overlap matrices corresponding to
the edge excitations of the parton states with a constrained number of
particles in the different parton Landau levels. Counting in these matches the
individual branches present in RSES, providing insight about how different
branches are formed
Impact of MgII interstellar medium absorption on near-ultraviolet exoplanet transit measurements
Ultraviolet (UV) transmission spectroscopy probes atmospheric escape, which
has a significant impact on planetary atmospheric evolution. If unaccounted
for, interstellar medium absorption (ISM) at the position of specific UV lines
might bias transit depth measurements, and thus potentially affect the
(non-)detection of features in transmission spectra. Ultimately, this is
connected to the so called ``resolution-linked bias'' (RLB) effect. We present
a parametric study quantifying the impact of unresolved or unconsidered ISM
absorption in transit depth measurements at the position of the MgII h&k
resonance lines (i.e. 2802.705 {\AA} and 2795.528 {\AA} respectively) in the
near-ultraviolet spectral range. We consider main-sequence stars of different
spectral types and vary the shape and amount of chromospheric emission, ISM
absorption, and planetary absorption, as well as their relative velocities. We
also evaluate the role played by integration bin and spectral resolution. We
present an open-source tool enabling one to quantify the impact of unresolved
or unconsidered MgII ISM absorption in transit depth measurements. We further
apply this tool to a few already or soon to be observed systems. On average, we
find that ignoring ISM absorption leads to biases in the MgII transit depth
measurements comparable to the uncertainties obtained from the observations
published to date. However, considering the bias induced by ISM absorption
might become necessary when analysing observations obtained with the next
generation space telescopes with UV coverage (e.g. LUVOIR, HABEX), which will
provide transmission spectra with significantly smaller uncertainties compared
to what obtained with current facilities (e.g. HST).Comment: Accepted for publication in MNRA
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