General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States

We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT), such as e.g. a general quantum Hall state. We demonstrate that for such states the reduced density matrix of a finite spatial region of the gapped topological state is a thermal density matrix of the chiral edge state CFT which would appear at the spatial boundary of that region. We obtain this result by applying a physical instantaneous cut to the gapped system, and by viewing the cutting process as a sudden "quantum quench" into a CFT, using the tools of boundary conformal field theory. We thus provide a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state.Comment: 7 pages, 2 figures. A presentation of this work can be found in the following talk at KITP: http://online.itp.ucsb.edu/online/compqcm10/qi

Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class

We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole sample even in the thermodynamic limit.Comment: 5 pages, 4 figure

A three-dimensional hydrodynamical line profile analysis of iron lines and barium isotopes in HD140283

Heavy-elements, i.e. those beyond the iron peak, mostly form via two neutron capture processes: the s- and r-process. Metal-poor stars should contain fewer isotopes that form via the s-process, according to currently accepted theory. It has been shown in several investigations that theory and observation do not agree well, raising questions on the validity of either the methodology or the theory. We analyse the metal-poor star HD140283, for which we have a high quality spectrum. We test whether a 3D LTE stellar atmosphere and spectrum synthesis code permits a more reliable analysis of the iron abundance and barium isotope ratio than a 1D LTE analysis. Using 3D model atmospheres, we examine 91 iron lines of varying strength and formation depth. This provides us with the star's rotational speed. With this, we model the barium isotope ratio by exploiting the hyperfine structure of the singly ionised 4554 resonance line, and study the impact of the uncertainties in the stellar parameters. HD140283's vsini = 1.65 +/- 0.05 km/s. Barium isotopes under the 3D paradigm show a dominant r-process signature as 77 +/- 6 +/- 17% of barium isotopes form via the r-process, where errors represent the assigned random and systematic errors, respectively. We find that 3D LTE fits reproduce iron line profiles better than those in 1D, but do not provide a unique abundance (within the uncertainties). However, we demonstrate that the isotopic ratio is robust against this shortcoming. Our barium isotope result agrees well with currently accepted theory regarding the formation of the heavy-elements during the early Galaxy. The improved fit to the asymmetric iron line profiles suggests that the current state of 3D LTE modelling provides excellent simulations of fluid flows. However, the abundances they provide are not yet self-consistent. This may improve with NLTE considerations and higher resolution models.Comment: 16 pages, 10 figures, 5 tables. Accepted for publication in A&

Phonon-mediated vs. Coulombic Back-Action in Quantum Dot circuits

Quantum point contacts (QPCs) are commonly employed to capacitively detect the charge state of coupled quantum dots (QD). An indirect back-action of a biased QPC onto a double QD laterally defined in a GaAs/AlGaAs heterostructure is observed. Energy is emitted by non-equilibrium charge carriers in the leads of the biased QPC. Part of this energy is absorbed by the double QD where it causes charge fluctuations that can be observed under certain conditions in its stability diagram. By investigating the spectrum of the absorbed energy, we identify both acoustic phonons and Coulomb interaction being involved in the back-action, depending on the geometry and coupling constants

The photospheric solar oxygen project: III. Investigation of the centre-to-limb variation of the 630nm [OI]-NiI blend

The solar photospheric abundance of oxygen is still a matter of debate. For about ten years some determinations have favoured a low oxygen abundance which is at variance with the value inferred by helioseismology. Among the oxygen abundance indicators, the forbidden line at 630nm has often been considered the most reliable even though it is blended with a NiI line. In Papers I and Paper II of this series we reported a discrepancy in the oxygen abundance derived from the 630nm and the subordinate [OI] line at 636nm in dwarf stars, including the Sun. Here we analyse several, in part new, solar observations of the the centre-to-limb variation of the spectral region including the blend at 630nm in order to separate the individual contributions of oxygen and nickel. We analyse intensity spectra observed at different limb angles in comparison with line formation computations performed on a CO5BOLD 3D hydrodynamical simulation of the solar atmosphere. The oxygen abundances obtained from the forbidden line at different limb angles are inconsistent if the commonly adopted nickel abundance of 6.25 is assumed in our local thermodynamic equilibrium computations. With a slightly lower nickel abundance, A(Ni)~6.1, we obtain consistent fits indicating an oxygen abundance of A(O)=8.73+/-0.05. At this value the discrepancy with the subordinate oxygen line remains. The derived value of the oxygen abundance supports the notion of a rather low oxygen abundance in the solar hotosphere. However, it is disconcerting that the forbidden oxygen lines at 630 and 636nm give noticeably different results, and that the nickel abundance derived here from the 630nm blend is lower than expected from other nickel lines.Comment: to appear in A&

A double-dot quantum ratchet driven by an independently biased quantum point contact

We study a double quantum dot (DQD) coupled to a strongly biased quantum point contact (QPC), each embedded in independent electric circuits. For weak interdot tunnelling we observe a finite current flowing through the unbiased Coulomb blockaded DQD in response to a strong bias on the QPC. The direction of the current through the DQD is determined by the relative detuning of the energy levels of the two quantum dots. The results are interpreted in terms of a quantum ratchet phenomenon in a DQD energized by a nearby QPC.Comment: revised versio