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 ($\hat{V}^\text{Pf}_3$) 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 $\hat{V}^\text{Pf}_3$ Hamiltonian.Comment: 15 pages, 10 figure

Candidate local parent Hamiltonian for 3/7 fractional quantum Hall effect

While a parent Hamiltonian for Laughlin $1/3$ 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 $n/(2n+1)$ with $n\geq2$. 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 $\nu=3/7$. We propose that adding an appropriately constructed three-body interaction yields the unprojected $3/7$ 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 $\phi_2^2$, $\phi_2^3$, and $\phi_3^2$, where $\phi_n$ is the wave function of $n$ 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