Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution

For the simulation of equilibrium states and finite-temperature response functions of strongly-correlated quantum many-body systems, we compare the efficiencies of two different approaches in the framework of the density matrix renormalization group (DMRG). The first is based on matrix product purifications. The second, more recent one, is based on so-called minimally entangled typical thermal states (METTS). For the latter, we highlight the interplay of statistical and DMRG truncation errors, discuss the use of self-averaging effects, and describe schemes for the computation of response functions. For critical as well as gapped phases of the spin-1/2 XXZ chain and the one-dimensional Bose-Hubbard model, we assess the computation costs and accuracies of the two methods at different temperatures. For almost all considered cases, we find that, for the same computation cost, purifications yield more accurate results than METTS -- often by orders of magnitude. The METTS algorithm becomes more efficient only for temperatures well below the system's energy gap. The exponential growth of the computation cost in the evaluation of response functions limits the attainable timescales in both methods and we find that in this regard, METTS do not outperform purifications.Comment: 12 pages + 4 pages appendix, 12 figures; minor improvements of data and text; published versio

Exemplary Design Research

In this paper, we will look at what role a research program and an interventionist research strategy based on design experiments may play for the advancement of knowledge relevant to design and designers. We suggest the notion of exemplary design research driven by programs and experiments and by this we refer to research based on the explicit formulation of design programs that act as a frame and foundation for carrying out series of design experiments. It is 'exemplary' in the sense that it enables critical dissemination primarily by creating examples of what could be done and how, i.e. examples that both express the possibilities and characteristics of the design program as well as more general suggestions about a certain (change to) design practice

New zero free regions for the derivatives of the Riemann zeta function

The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the right half-plane where these derivatives cannot have any zeros; and then, in the rare regions of the complex plane that do contain zeros of the k-th derivative of the zeta function, we describe a unexpected phenomenon, which implies great regularities in their zero distributions. In particular, we prove sharp estimates for the number of zeros in each of these new critical strips, and we explain how they converge, in a very precise, periodic fashion, to their central, critical lines, as k increases. This not only shows that the zeros are not randomly scattered to the right of the line Re(s)=1, but that, in many respects, their two-dimensional distribution eventually becomes much simpler and more predictable than the one-dimensional behavior of the zeros of the zeta function on the line Re(s)=1/2

Studies on the sucrose binding site of the glucosyltransferases of Leuconostoc and Streptococcus bacteria

para-Nitrophenyl-(alpha)-D-glucopyranoside was found to be a substrate for the glucosyltransferases produced by several species of Streptococcus and Leuconostoc bacteria. It was found to react to produce both high molecular weight dextran and acceptor products with the glucosyltransferase of Leuconostoc mesenteroide B512F;The glucosyltransferases were also found to react with alternate glucosyl donors such as dextran, maltotriose, panose, and isomaltodextrins containing three or more glucose units. These reactions seemed to be the reverse of acceptor reactions;In order to study the sucrose binding sites of these enzymes, techniques were developed for the synthesis of sucrose analogs. By these techniques, we synthesized 6-deoxysucrose, 6-thiosucrose, 3-deoxysucrose, 3-deoxy-3-fluorosucrose, and allosucrose;The sucrose analogs were tested as substrates and/or inhibitors of the glucosyltransferases synthesized by Streptococcus mutans 6715, GTF-I which synthesizes a water insoluble glucan, and GTF-S which synthesizes a water soluble glucan. 6-Thiosucrose, 3-deoxysucrose, and 3-deoxy-3-fluorosucrose were all glycosyl donors for both enzymes as judged by the formation of acceptor products with maltose. All of the analogs were inhibitors to some extent for the enzymes. The best inhibitor was 6-deoxysucrose with a competitive K(,I) one order of magnitude lower than the K(,m) for sucrose

Structural Properties of Two-Dimensional Polymers

We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and compared to the results of percolation theory. We also describe the dependence of the typical cluster structures on the reaction rate.Comment: 7 pages, LaTeX with RevTeX and epsf styles and PostScript figures included (uuencoded shell archive), TVP-93051

Optimal stochastic modelling with unitary quantum dynamics

Identifying and extracting the past information relevant to the future behaviour of stochastic processes is a central task in the quantitative sciences. Quantum models offer a promising approach to this, allowing for accurate simulation of future trajectories whilst using less past information than any classical counterpart. Here we introduce a class of phase-enhanced quantum models, representing the most general means of causal simulation with a unitary quantum circuit. We show that the resulting constructions can display advantages over previous state-of-art methods - both in the amount of information they need to store about the past, and in the minimal memory dimension they require to store this information. Moreover, we find that these two features are generally competing factors in optimisation - leading to an ambiguity in what constitutes the optimal model - a phenomenon that does not manifest classically. Our results thus simultaneously offer new quantum advantages for stochastic simulation, and illustrate further qualitative differences in behaviour between classical and quantum notions of complexity.Comment: 9 pages, 5 figure