Particle number conservation in quantum many-body simulations with matrix product operators

Incorporating conservation laws explicitly into matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in simulation where the dynamically evolving entities are matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that in this case often the entanglement imposed by the global constraint of fixed particle number is the limiting factor.Comment: minor changes, 18 pages, 5 figure

Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit

We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the thermodynamic limit. The BMPS is built on a dual series of reduced biorthonormal bases for the left and right Perron states of a non-Hermitian matrix. We propose two alternative infinite-size Biorthonormal TMRG (iBTMRG) algorithms and compare their numerical performance in both finite and infinite systems. We show that both iBTMRGs produce a dual infinite-BMPS (iBMPS) which are translationally invariant in the thermodynamic limit. We also develop an efficient wave function transformation of the iBTMRG, an analogy of McCulloch in the infinite-DMRG [arXiv:0804.2509 (2008)], to predict the wave function as the lattice size is increased. The resulting iBMPS allows for probing bulk properties of the system in the thermodynamic limit without boundary effects and allows for reducing the computational cost to be independent of the lattice size, which are illustrated by calculating the magnetization as a function of the temperature and the critical spin-spin correlation in the thermodynamic limit for a 2D classical Ising model.Comment: 14 pages, 9 figure

Genome-wide mapping reveals single-origin chromosome replication in Leishmania, a eukaryotic microbe

Background DNA replication initiates on defined genome sites, termed origins. Origin usage appears to follow common rules in the eukaryotic organisms examined to date: all chromosomes are replicated from multiple origins, which display variations in firing efficiency and are selected from a larger pool of potential origins. To ask if these features of DNA replication are true of all eukaryotes, we describe genome-wide origin mapping in the parasite Leishmania. Results Origin mapping in Leishmania suggests a striking divergence in origin usage relative to characterized eukaryotes, since each chromosome appears to be replicated from a single origin. By comparing two species of Leishmania, we find evidence that such origin singularity is maintained in the face of chromosome fusion or fission events during evolution. Mapping Leishmania origins suggests that all origins fire with equal efficiency, and that the genomic sites occupied by origins differ from related non-origins sites. Finally, we provide evidence that origin location in Leishmania displays striking conservation with Trypanosoma brucei, despite the latter parasite replicating its chromosomes from multiple, variable strength origins. Conclusions The demonstration of chromosome replication for a single origin in Leishmania, a microbial eukaryote, has implications for the evolution of origin multiplicity and associated controls, and may explain the pervasive aneuploidy that characterizes Leishmania chromosome architecture

Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime ($0<\alpha\le 2$). In this paper we illustrate that widely used tail index estimates (log-log linear regression and Hill) can give exponents well above the asymptotic limit for $\alpha$ close to 2, resulting in overestimation of the tail exponent in finite samples. The reported value of the tail exponent $\alpha$ around 3 may very well indicate a Levy-stable distribution with $\alpha\approx 1.8$.Comment: To be published in Int. J. Modern Physics C (2001) vol. 12 no.

Development and application of operational techniques for the inventory and monitoring of resources and uses for the Texas coastal zone. Volume 1: Text

The author has identified the following significant results. Image interpretation and computer-assisted techniques were developed to analyze LANDSAT scenes in support of resource inventory and monitoring requirements for the Texas coastal region. Land cover and land use maps, at a scale of 1:125,000 for the image interpretation product and 1:24,000 for the computer-assisted product, were generated covering four Texas coastal test sites. Classification schemes which parallel national systems were developed for each procedure, including 23 classes for image interpretation technique and 13 classes for the computer-assisted technique. Results indicate that LANDSAT-derived land cover and land use maps can be successfully applied to a variety of planning and management activities on the Texas coast. Computer-derived land/water maps can be used with tide gage data to assess shoreline boundaries for management purposes

Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study

We study the phase diagram of a frustrated spin-1/2 ferromagnetic chain with anisotropic exchange interactions in an external magnetic field, using the density matrix renormalization group method. We show that an easy-axis anisotropy enhances the tendency towards multimagnon bound states, while an easy-plane anisotropy favors chirally ordered phases. In particular, a moderate easy-plane anisotropy gives rise to a quantum phase transition at intermediate magnetization. We argue that this transition is related to the finite-field phase transition experimentally observed in the spin-1/2 compound LiCuVO_4.Comment: The final published versio

How much progress do children in Shanghai make over one academic year? Evidence from PISA

Since its entry into the Programme for International Student Assessment (PISA) in 2009, the Chinese province of Shanghai has been the top-performing economy within these international rankings. Many have interpreted this as demonstrating how Shanghai has a “world class” education system, the most effective teaching methods, and the best schools. This article questions such interpretations of the PISA results. Specifically, we argue that statements about school and school system quality require information on the progress that children make during their time at school, which the PISA rankings do not provide (at least not directly). Our empirical analysis then uses a “fuzzy” regression discontinuity design approach to demonstrate how a rather different perspective of Shanghai’s performance in PISA emerges once pupils’ academic progress over one particular school year is considered. Our key finding is that the first year of upper secondary school in Shanghai adds essentially no value (on average) to children’s PISA reading, science, and mathematics test scores

Warren McCulloch and the British cyberneticians

Warren McCulloch was a significant influence on a number of British cyberneticians, as some British pioneers in this area were on him. He interacted regularly with most of the main figures on the British cybernetics scene, forming close friendships and collaborations with several, as well as mentoring others. Many of these interactions stemmed from a 1949 visit to London during which he gave the opening talk at the inaugural meeting of the Ratio Club, a gathering of brilliant, mainly young, British scientists working in areas related to cybernetics. This paper traces some of these relationships and interaction