Real-Space Entanglement Spectrum of Quantum Hall States

We investigate the entanglement spectra arising from sharp real-space partitions of the system for quantum Hall states. These partitions differ from the previously utilized orbital and particle partitions and reveal complementary aspects of the physics of these topologically ordered systems. We show, by constructing one to one maps to the particle partition entanglement spectra, that the counting of the real-space entanglement spectra levels for different particle number sectors versus their angular momentum along the spatial partition boundary is equal to the counting of states for the system with a number of (unpinned) bulk quasiholes excitations corresponding to the same particle and flux numbers. This proves that, for an ideal model state described by a conformal field theory, the real-space entanglement spectra level counting is bounded by the counting of the conformal field theory edge modes. This bound is known to be saturated in the thermodynamic limit (and at finite sizes for certain states). Numerically analyzing several ideal model states, we find that the real-space entanglement spectra indeed display the edge modes dispersion relations expected from their corresponding conformal field theories. We also numerically find that the real-space entanglement spectra of Coulomb interaction ground states exhibit a series of branches, which we relate to the model state and (above an entanglement gap) to its quasiparticle-quasihole excitations. We also numerically compute the entanglement entropy for the nu=1 integer quantum Hall state with real-space partitions and compare against the analytic prediction. We find that the entanglement entropy indeed scales linearly with the boundary length for large enough systems, but that the attainable system sizes are still too small to provide a reliable extraction of the sub-leading topological entanglement entropy term.Comment: 13 pages, 11 figures; v2: minor corrections and formatting change

Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

In this letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read state expected to describe the observed FQHE plateau at nu=5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et. al. are also addressed.Comment: 5 pages, 2 eps figures v2: A few minor changes and citation corrections. In particular, the connection to cond-mat/9711087 has been clarified. v3: Minor changes: fixed references to Fig. 2, updated citations, changed a few words to conform to the version published in PR

Numerical analysis to quantify the influence of smear zone characteristics on preloading design in soft clay

In this paper, the effects of uncertainties of smear zone characteristics induced by installation of prefabricated vertical drains on the preloading design are numerically investigated. FLAC 2D finite difference software with additional developed subroutines has been employed to conduct the numerical simulations. The finite difference analyses have been verified using a case study. Furthermore, a comprehensive parametric study is conducted to investigate the influence of smear zone permeability and extent on the model predictions. Results of this study indicate that the assumptive properties for smear zone characteristics may result in inaccurate predictions of ground deformations and pore water pressures. This may lead to early removal of the surcharge in the construction process causing excessive post construction settlement. It is recommended to practising engineers to use results of trial preloading to back calculate the required smear zone characteristics in the early stages of embankment construction to optimize the design

Uncertainties of Smear Zone Characteristics in the Design of Preloading with Prefabricated Vertical Drains

Installing prefabricated vertical drains using mandrels induces disturbance of the soil surrounding the drain, resulting in a smear zone with the reduced permeability. The required time for pore pressure dissipation in preloading design is strongly associated with the smear zone characteristics. In this study, the effects of smear zone properties on preloading time are numerically investigated. Parametric study is conducted to find out the range of smear zone parameters significantly influencing the consolidation period. It is observed that the characteristics of smear zone namely size and permeability have a substantial impact on the preloading design to achieve certain soil strength and stiffness satisfying both bearing capacity and settlement design criteria

Coulomb Blockade Doppelgangers in Quantum Hall States

In this paper, we ask the question: How well can Coulomb blockade experiments correctly identify and distinguish between different topological orders in quantum Hall states? We definitively find the answer to be: Quite poorly. In particular, we write the general expression for the spacing of resonance peaks in a simple form that explicitly displays its dependence on the conformal scaling dimensions of the systems' edge modes. This form makes transparent the general argument that the Coulomb blockade peak spacings do not provide a strongly indicative signature of the topological order of the system, since it is only weakly related to the braiding statistics. We bolster this general argument with examples for all the most physically relevant non-Abelian candidate states, demonstrating that they have Coulomb blockade doppelgangers -- candidate states at the same filling fraction with identical Coulomb blockade signatures, but dramatically different topological orders and braiding statistics.Comment: 12 pages, 1 figure; portions of this paper were formerly included in Appendix C of arXiv:0903.3108; v2: examples added, minor corrections made; v3: discussions of non-uniform filling and of hierarchical counterparts of multi-component states added, minor corrections mad

Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States

We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction nu=5/2. We complete the program started in Nucl. Phys. B 506, 685 (1997) and show that the degenerate four-quasihole and six-quasihole wavefunctions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+1/2 conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wavefunctions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wavefunctions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wavefunction and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.Comment: 68 pages, 3 figures; v2: substantial revisions and additions for clarity, minor correction

Analyzing consolidation data to predict smear zone characteristics induced by vertical drain installation for soft soil improvement

In this paper, the effects of variability of smear zone characteristics induced by installation of prefabricated vertical drains on the preloading design are investigated employing analytical and numerical approaches. Conventional radial consolidation theory has been adopted to conduct analytical parametric studies considering variations of smear zone permeability and extent. FLAC 2D finite difference software has been employed to conduct the numerical simulations. The finite difference analyses have been verified using three case studies including two embankments and a large-scale laboratory consolidometer with a central geosynthetic vertical drain. A comprehensive numerical parametric study is conducted to investigate the influence of smear zone permeability and extent on the model predictions. Furthermore, the construction of the trial embankment is recommended as a reliable solution to estimate accurate smear zone properties and minimise the post construction settlement. A back-calculation procedure is employed to determine the minimum required waiting time after construction of the trial embankment to predict the smear zone characteristics precisely. Results of this study indicate that the accurate smear zone permeability and extent can be back-calculated when 30% degree of consolidation is obtained after construction of the trial embankment. © 2014 Techno-Press, Ltd

Nuclear Activity and the Conditions of Star-formation at the Galactic Center

The Galactic Center is the closest galactic nucleus that can be studied with unprecedented angular resolution and sensitivity. We summarize recent basic observational results on Sagittarius A* and the conditions for star formation in the central stellar cluster. We cover results from the radio, infrared, and X-ray domain and include results from simulation as well. From (sub-)mm and near-infrared variability and near-infrared polarization data we find that the SgrA* system (supermassive black hole spin, a potential temporary accretion disk and/or outflow) is well ordered in its geometrical orientation and in its emission process that we assume to reflect the accretion process onto the supermassive black hole (SMBH).Comment: 11 pages, 4 figures, 1 table; published in PoS-SISSA Proceedings of the: Frontier Research in Astrophysics - II, 23-28 May 2016, Mondello (Palermo), Ital