From density-matrix renormalization group to matrix product states

In this paper we give an introduction to the numerical density matrix renormalization group (DMRG) algorithm, from the perspective of the more general matrix product state (MPS) formulation. We cover in detail the differences between the original DMRG formulation and the MPS approach, demonstrating the additional flexibility that arises from constructing both the wavefunction and the Hamiltonian in MPS form. We also show how to make use of global symmetries, for both the Abelian and non-Abelian cases.Comment: Numerous small changes and clarifications, added a figur

Symmetry adapted finite-cluster solver for quantum Heisenberg model in two-dimensions: a real-space renormalization approach

We present a quantum cluster solver for spin-$S$ Heisenberg model on a two-dimensional lattice. The formalism is based on the real-space renormalization procedure and uses the lattice point group-theoretical analysis and nonabelian SU(2) spin symmetry technique. The exact diagonalization procedure is used twice at each renormalization group step. The method is applied to the spin-half antiferromagnet on a square lattice and a calculation of local observables is demonstrated. A symmetry based truncation procedure is suggested and verified numerically.Comment: willm appear in J. Phys.

Predicting the Starquakes in PSR J0537-6910

We report on more than 7 years of monitoring of PSR J0537-6910, the 16 ms pulsar in the Large Magellanic Cloud, using data acquired with the RXTE. During this campaign the pulsar experienced 23 sudden increases in frequency (``glitches'') amounting to a total gain of over six ppm of rotation frequency superposed on its gradual spindown of d(nu)/d(t) = -2e-10 Hz/s. The time interval from one glitch to the next obeys a strong linear correlation to the amplitude of the first glitch, with a mean slope of about 400 days ppm (6.5 days per uHz), such that these intervals can be predicted to within a few days, an accuracy which has never before been seen in any other pulsar. There appears to be an upper limit of ~40 uHz for the size of glitches in_all_ pulsars, with the 1999 April glitch of J0537 as the largest so far. The change in the spindown of J0537 across the glitches, Delta(d(nu)/d(t)), appears to have the same hard lower limit of -1.5e-13 Hz/s, as, again, that observed in all other pulsars. The spindown continues to increase in the long term, d(d(nu)/d(t))/d(t) = -1e-21 Hz/s/s, and thus the timing age of J0537 (-0.5 nu d(nu)/d(t)) continues to decrease at a rate of nearly one year every year, consistent with movement of its magnetic moment away from its rotational axis by one radian every 10,000 years, or about one meter per year. J0537 was likely to have been born as a nearly-aligned rotator spinning at 75-80 Hz, with a |d(nu)/d(t)| considerably smaller than its current value of 2e-10 Hz/s. The pulse profile of J0537 consists of a single pulse which is found to be flat at its peak for at least 0.02 cycles.Comment: 54 pages, 12 figures. Accepted for publication in The Astrophysical Journal. Cleaner figure 2. V4 -- in line with version accepted by Ap

What does my patient's coronary artery calcium score mean? Combining information from the coronary artery calcium score with information from conventional risk factors to estimate coronary heart disease risk

Abstract: Background: The coronary artery calcium (CAC) score is an independent predictor of coronary heart disease. We sought to combine information from the CAC score with information from conventional cardiac risk factors to produce post-test risk estimates, and to determine whether the score may add clinically useful information. Methods: We measured the independent cross-sectional associations between conventional cardiac risk factors and the CAC score among asymptomatic persons referred for non-contrast electron beam computed tomography. Using the resulting multivariable models and published CAC score-specific relative risk estimates, we estimated post-test coronary heart disease risk in a number of different scenarios. Results: Among 9341 asymptomatic study participants (age 35-88 years, 40% female), we found that conventional coronary heart disease risk factors including age, male sex, self-reported hypertension, diabetes and high cholesterol were independent predictors of the CAC score, and we used the resulting multivariable models for predicting post-test risk in a variety of scenarios. Our models predicted, for example, that a 60-year-old non-smoking non-diabetic women with hypertension and high cholesterol would have a 47% chance of having a CAC score of zero, reducing her 10-year risk estimate from 15% (per Framingham) to 6-9%; if her score were over 100, however (a 17% chance), her risk estimate would be markedly higher (25-51% in 10 years). In low risk scenarios, the CAC score is very likely to be zero or low, and unlikely to change management. Conclusion: Combining information from the CAC score with information from conventional risk factors can change assessment of coronary heart disease risk to an extent that may be clinically important, especially when the pre-test 10-year risk estimate is intermediate. The attached spreadsheet makes these calculations easy

The Role of Side Chains and Hydration on Mixed Charge Transport in <i>n</i> ‐Type Polymer Films

Introducing ethylene glycol (EG) side chains to a conjugated polymer backbone is a well‐established synthetic strategy for designing organic mixed ion‐electron conductors (OMIECs). However, the impact that film swelling has on mixed conduction properties has yet to be scoped, particularly for electron‐transporting (n‐type) OMIECs. Here, the authors investigate the effect of the length of branched EG chains on mixed charge transport of n‐type OMIECs based on a naphthalene‐1,4,5,8‐tetracarboxylic‐diimide‐bithiophene backbone. Atomic force microscopy (AFM), grazing‐incidence wide‐angle X‐ray scattering (GIWAXS), and scanning tunneling microscopy (STM) are used to establish the similarities between the common‐backbone films in dry conditions. Electrochemical quartz crystal microbalance with dissipation monitoring (EQCM‐D) and in situ GIWAXS measurements reveal stark changes in film swelling properties and microstructure during electrochemical doping, depending on the side chain length. It is found that even in the loss of the crystallite content upon contact with the aqueous electrolyte, the films can effectively transport charges and that it is rather the high water content that harms the electronic interconnectivity within the OMIEC films. These results highlight the importance of controlling water uptake in the films to impede charge transport in n‐type electrochemical devices

Sino-UK educational differences: the impacts of cultures and the current educational curricular on students in computer science

With the increased worldwide mobility of students, the need to understand the impact of different cultures and educational curricular also increases. This chapter focuses on how the National University Entrance Examination or Gaokao and Confucianism influence the way Chinese students learn. Questionnaires were distributed to senior secondary school students, undergraduate students and parents both in China and the UK with the aim of understanding their decision-making processes regarding their education, as well as their views on the quality of the degrees from different Asian and European countries. The views of lecturers from both China and the UK were also obtained with regard to student’s proficiency in Mathematics and Computer Science, as well as how their receiving and transmitting skills in English may impact the learning of students from different Asian and European countries. The findings show that parents shape student’s educational development choices through their investments which may have been influenced by their cultures. Compared to other Asian and European students, the English language skills of Chinese students are lower; however according to their educators, this does not impact how well they can learn in subject areas such as Computer Science. For British higher education institutes to maintain their brand image as the most celebrated and respected education providers in China, some adjustments should be made to those that deliver UK content to Chinese students

Super-diffusive Transport Processes in Porous Media

The basic assumption of models for the transport of contaminants through soil is that the movements of solute particles are characterized by the Brownian motion. However, the complexity of pore space in natural porous media makes the hypothesis of Brownian motion far too restrictive in some situations. Therefore, alternative models have been proposed. One of the models, many times encountered in hydrology, is based in fractional differential equations, which is a one-dimensional fractional advection diffusion equation where the usual second-order derivative gives place to a fractional derivative of order α, with 1 < α ≤ 2. When a fractional derivative replaces the second-order derivative in a diffusion or dispersion model, it leads to anomalous diffusion, also called super-diffusion. We derive analytical solutions for the fractional advection diffusion equation with different initial and boundary conditions. Additionally, we analyze how the fractional parameter α affects the behavior of the solutions

Binding Energy of Charged Excitons in ZnSe-based Quantum Wells

Excitons and charged excitons (trions) are investigated in ZnSe-based quantum well structures with (Zn,Be,Mg)Se and (Zn,Mg)(S,Se) barriers by means of magneto-optical spectroscopy. Binding energies of negatively () and positively (X+) charged excitons are measured as functions of quantum well width, free carrier density and in external magnetic fields up to 47 T. The binding energy of shows a strong increase from 1.4 to 8.9 meV with decreasing quantum well width from 190 to 29 A. The binding energies of X+ are about 25% smaller than the binding energy in the same structures. The magnetic field behavior of and X+ binding energies differ qualitatively. With growing magnetic field strength, increases its binding energy by 35-150%, while for X+ it decreases by 25%. Zeeman spin splittings and oscillator strengths of excitons and trions are measured and discussed

The density-matrix renormalization group

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly acquired the status of method of choice for numerical studies of one-dimensional quantum systems. Its applications to the calculation of static, dynamic and thermodynamic quantities in such systems are reviewed. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and non-equilibrium statistical physics, and time-dependent phenomena is discussed. This review also considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the January 2005 issu