Simulation of anyons with tensor network algorithms

Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but numerical tools for studying them are as yet limited. We show how existing tensor network algorithms may be adapted for use with systems of anyons, and demonstrate this process for the 1-D Multi-scale Entanglement Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of interacting Fibonacci anyons, computing their scaling dimensions and local scaling operators. The scaling dimensions obtained are seen to be in agreement with conformal field theory. The techniques developed are applicable to any tensor network algorithm, and the ability to adapt these ansaetze for use on anyonic systems opens the door for numerical simulation of large systems of free and interacting anyons in one and two dimensions.Comment: Fixed typos, matches published version. 16 pages, 21 figures, 4 tables, RevTeX 4-1. For a related work, see arXiv:1006.247

Boundary quantum critical phenomena with entanglement renormalization

We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. Our construction, valid for arbitrary critical systems, produces an effective chain with explicit separation of energy scales that relates to Wilson's RG formulation of the Kondo problem. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.Comment: 8 pages, 12 figures, for a related work see arXiv:0912.289

First order wetting of rough substrates and quantum unbinding

Replica and functional renormalization group methods show that, with short range substrate forces or in strong fluctuation regimes, wetting of a self-affine rough wall in 2D turns first-order as soon as the wall roughness exponent exceeds the anisotropy index of bulk interface fluctuations. Different thresholds apply with long range forces in mean field regimes. For bond-disordered bulk, fixed point stability suggests similar results, which ultimately rely on basic properties of quantum bound states with asymptotically power-law repulsive potentials.Comment: 11 pages, 1 figur

Correlation length by measuring empty space in simulated aggregates

We examine the geometry of the spaces between particles in diffusion-limited cluster aggregation, a numerical model of aggregating suspensions. Computing the distribution of distances from each point to the nearest particle, we show that it has a scaled form independent of the concentration phi, for both two- (2D) and three-dimensional (3D) model gels at low phi. The mean remoteness is proportional to the density-density correlation length of the gel, xi, allowing a more precise measurement of xi than by other methods. A simple analytical form for the scaled remoteness distribution is developed, highlighting the geometrical information content of the data. We show that the second moment of the distribution gives a useful estimate of the permeability of porous media.Comment: 4 page

Numerical study of multilayer adsorption on fractal surfaces

We report a numerical study of van der Waals adsoprtion and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distributin of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to crossover effects, consistent with the findings of recent experiments. The effects of pore coupling and curvature dependent surface tension were also studied.Comment: 11 pages, 3 figure

He Scattering from Random Adsorbates, Disordered Compact Islands and Fractal Submonolayers: Intensity Manifestations of Surface Disorder

A theoretical study is made on He scattering from three fundamental classes of disordered ad-layers: (a) Translationally random adsorbates, (b) disordered compact islands and (c) fractal submonolayers. The implications of the results to experimental studies of He scattering from disordered surfaces are discussed, and a combined experimental-theoretical study is made for Ag submonolayers on Pt(111). Some of the main theoretical findings are: (1) Structural aspects of the calculated intensities from translationally random clusters were found to be strongly correlated with those of individual clusters. (2) Low intensity Bragg interference peaks appear even for scattering from very small ad-islands, and contain information on the ad-island local electron structure. (3) For fractal islands, just as for islands with a different structure, the off-specular intensity depends on the parameters of the He/Ag interaction, and does not follow a universal power law as previously proposed in the literature. In the experimental-theoretical study of Ag on Pt(111), we use first experimental He scattering data from low-coverage (single adsorbate) systems to determine an empirical He/Ag-Pt potential of good quality. Then, we carry out He scattering calculations for high coverage and compare with experiments. The conclusions are that the actual experimental phase corresponds to small compact Ag clusters of narrow size distribution, translationally disordered on the surface.Comment: 36 double-spaced pages, 10 figures; accepted by J. Chem. Phys., scheduled to appear March 8. More info available at http://www.fh.huji.ac.il/~dani

Schrodinger equation for the one particle density matrix of thermal systems: An alternative formulation of Bose-Einstein condensation

We formulate a linear Schrodinger equation with the temperature-dependent potential for the one-particle density matrix and obtain the condensation temperature of the Bose-Einstein condensate from a bound-state condition for the Schrodinger equation both with and without the confining trap. The results are in very good agreement with those of the full statistical physics treatment. This is an alternative to the Bose-Einstein condensation in the standard ideal Bose gas treatment.Comment: 4 pages, 2 figure

Structure of the 26S proteasome with ATP-gamma S bound provides insights into the mechanism of nucleotide-dependent substrate translocation

The 26S proteasome is a 2.5-MDa, ATP-dependent multisubunit proteolytic complex that processively destroys proteins carrying a degradation signal. The proteasomal ATPase heterohexamer is a key module of the 19S regulatory particle; it unfolds substrates and translocates them into the 20S core particle where degradation takes place. We used cryoelectron microscopy single-particle analysis to obtain insights into the structural changes of 26S proteasome upon the binding and hydrolysis of ATP. The ATPase ring adopts at least two distinct helical staircase conformations dependent on the nucleotide state. The transition from the conformation observed in the presence of ATP to the predominant conformation in the presence of ATP-gamma S induces a sliding motion of the ATPase ring over the 20S core particle ring leading to an alignment of the translocation channels of the ATPase and the core particle gate, a conformational state likely to facilitate substrate translocation. Two types of inter-subunit modules formed by the large ATPase domain of one ATPase subunit and the small ATPase domain of its neighbor exist. They resemble the contacts observed in the crystal structures of ClpX and proteasome-activating nucleotidase, respectively. The ClpX-like contacts are positioned consecutively and give rise to helical shape in the hexamer, whereas the proteasome-activating nucleotidase-like contact is required to close the ring. Conformational switching between these forms allows adopting different helical conformations in different nucleotide states. We postulate that ATP hydrolysis by the regulatory particle ATPase (Rpt) 5 subunit initiates a cascade of conformational changes, leading to pulling of the substrate, which is primarily executed by Rpt1, Rpt2, and Rpt6

Effect of maternal age on ATP content and distribution of mitochondria in bovine oocytes.

Our objective was to understand how maternal age influences the mitochondrial population and ATP content of in vivo matured bovine oocytes

Deep classification of a large cryo-EM dataset defines the conformational landscape of the 26S proteasome

The 26S proteasome is a 2.5 MDa molecular machine that executes the degradation of substrates of the ubiquitin-proteasome pathway. The molecular architecture of the 26S proteasome was recently established by cryo-EM approaches. For a detailed understanding of the sequence of events from the initial binding of polyubiquitylated substrates to the translocation into the proteolytic core complex, it is necessary to move beyond static structures and characterize the conformational landscape of the 26S proteasome. To this end we have subjected a large cryo-EM dataset acquired in the presence of ATP and ATP-gamma S to a deep classification procedure, which deconvolutes coexisting conformational states. Highly variable regions, such as the density assigned to the largest subunit, Rpn1, are now well resolved and rendered interpretable. Our analysis reveals the existence of three major conformations: in addition to the previously described ATP-hydrolyzing (ATP(h)) and ATP-gamma S conformations, an intermediate state has been found. Its AAA-ATPase module adopts essentially the same topology that is observed in the ATP(h) conformation, whereas the lid is more similar to the ATP-gamma S bound state. Based on the conformational ensemble of the 26S proteasome in solution, we propose a mechanistic model for substrate recognition, commitment, deubiquitylation, and translocation into the core particle