Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets

When one tries to simulate quantum spin systems by the Monte Carlo method, often the 'minus-sign problem' is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed how to avoid the minus sign problem for certain class of frustrated Heisenberg models. The systems where this method is applicable are, for instance, the pyrochlore lattice and the $J_1-J_2$ Heisenberg model. The method works in singlet sector. It relies on expression of wave functions in dimer (pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In such a formulation, matrix elements of the exponent of Hamiltonian are positive.Comment: 19 LaTeX pages, 6 figures, 1 tabl

Structure and optical properties of high light output halide scintillators

Structural and optical properties of several high light output halide scintillators and closely related materials are presented based on first principles calculations. The optical properties are based on the Engel-Vosko generalized gradient approximation and the recently developed density functional of Tran and Blaha. The materials investigated are BaBr$_2$, BaIBr, BaCl$_2$, BaF$_2$, BaI$_2$, BiI$_3$, CaI$_2$, Cs$_2LiYCl$_6$, CsBa$_2$Br$_5$, CsBa$_2$I$_5$, K$_2$LaBr$_5$, K$_2$LaCl$_5$,K$_2$LaI$_5$, LaBr$_3$, LaCl$_3$, SrBr$_2$, and YI$_3$. For comparison results are presented for the oxide CdWO$_4$. We find that the Tran Blaha functional gives greatly improved band gaps and optical properties in this class of materials. Furthermore, we find that unlike CdWO$_4$, most of these halides are highly isotropic from an optical point of view even though in many cases the crystal structures and other properties are not. This general result is rationalized in terms of halide chemistry. Implications for the development of ceramic halide scintillators are discussed

Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm to find the low-lying spectrum of a Hamiltonian. While the number of elementary quantum gates does scale polynomially with the size of the system, it increases inversely to the desired error bound $\epsilon$. Making such simulations robust to decoherence using fault-tolerance constructs requires an additional factor of $1/ \epsilon$ gates. These constraints are illustrated by using a three qubit nuclear magnetic resonance system to simulate a pairing Hamiltonian, following the algorithm proposed by Wu, Byrd, and Lidar.Comment: 6 pages, 2 eps figure

Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.

On the Sign Problem in the Hirsch-Fye Algorithm for Impurity Problems

We show that there is no fermion sign problem in the Hirsch and Fye algorithm for the single-impurity Anderson model. Beyond the particle-hole symmetric case for which a simple proof exists, this has been known only empirically. Here we prove the nonexistence of a sign problem for the general case by showing that each spin trace for a given Ising configuration is separately positive. We further use this insight to analyze under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign.Comment: 2 pages, no figure; published versio

Efficiency of symmetric targeting for finite-T DMRG

Two targeting schemes have been known for the density matrix renormalization group (DMRG) applied to non-Hermitian problems; one uses an asymmetric density matrix and the other uses symmetric density matrix. We compare the numerical efficiency of these two targeting schemes when they are used for the finite temperature DMRG.Comment: 4 pages, 3 Postscript figures, REVTe

Neutron-proton analyzing power at 12 MeV and inconsistencies in parametrizations of nucleon-nucleon data

We present the most accurate and complete data set for the analyzing power Ay(theta) in neutron-proton scattering. The experimental data were corrected for the effects of multiple scattering, both in the center detector and in the neutron detectors. The final data at En = 12.0 MeV deviate considerably from the predictions of nucleon-nucleon phase-shift analyses and potential models. The impact of the new data on the value of the charged pion-nucleon coupling constant is discussed in a model study.Comment: Six pages, four figures, one table, to be published in Physics Letters

Modelling the cost-effectiveness of catch-up 'MenB' (Bexsero) vaccination in England

We assessed the cost-effectiveness of offering catch-up vaccination with Bexsero against meningococcal disease to children too old to receive the vaccine under the recently introduced infant programme. Offering catch-up vaccination to increasingly older children is less economically attractive because of declining disease burden. We estimate catch-up vaccination of 1year old children could be cost-effective, incremental on the infant programme with a vaccine price of ⩽£8 per dose. Extending vaccination to 2year olds could only be cost-effective (incremental on infant and 1year old catch-up) with a vaccine price of ⩽£3 per dose and was not cost-effective in sensitivity analyses with more conservative vaccine assumptions. Extending catch-up further to 3-4year olds was not cost-effective. Employing the current criteria for assessing vaccines, our models suggest that even with low vaccine prices only catch-up vaccination in 1year old children could be cost-effective, when considered incrementally on the infant programme.The research was funded by the National Institute for Health Research Health Protection Research Unit (NIHR HPRU) in Evaluation of Interventions at the University of Bristol in partnership with Public Health England (PHE)

Monte Carlo Study of the Separation of Energy Scales in Quantum Spin 1/2 Chains with Bond Disorder

One-dimensional Heisenberg spin 1/2 chains with random ferro- and antiferromagnetic bonds are realized in systems such as $Sr_3 CuPt_{1-x} Ir_x O_6$. We have investigated numerically the thermodynamic properties of a generic random bond model and of a realistic model of $Sr_3 CuPt_{1-x} Ir_x O_6$ by the quantum Monte Carlo loop algorithm. For the first time we demonstrate the separation into three different temperature regimes for the original Hamiltonian based on an exact treatment, especially we show that the intermediate temperature regime is well-defined and observable in both the specific heat and the magnetic susceptibility. The crossover between the regimes is indicated by peaks in the specific heat. The uniform magnetic susceptibility shows Curie-like behavior in the high-, intermediate- and low-temperature regime, with different values of the Curie constant in each regime. We show that these regimes are overlapping in the realistic model and give numerical data for the analysis of experimental tests.Comment: 7 pages, 5 eps-figures included, typeset using JPSJ.sty, accepted for publication in J. Phys. Soc. Jpn. 68, Vol. 3. (1999

Continuity of Local Time: An applied perspective

Continuity of local time for Brownian motion ranks among the most notable mathematical results in the theory of stochastic processes. This article addresses its implications from the point of view of applications. In particular an extension of previous results on an explicit role of continuity of (natural) local time is obtained for applications to recent classes of problems in physics, biology and finance involving discontinuities in a dispersion coefficient. The main theorem and its corollary provide physical principles that relate macro scale continuity of deterministic quantities to micro scale continuity of the (stochastic) local time.Comment: To appear in: "The fascination of Probability, Statistics and Their Applications. In honour of Ole E. Barndorff-Nielsen on his 80th birthday