Bond excitations in the pseudogap phase of the Hubbard Model

Using the dynamical cluster approximation, we calculate the correlation functions associated with the nearest neighbor bond operator which measure the z component of the spin exchange in the two-dimensional Hubbard model with $U$ equal to the bandwidth. We find that in the pseudogap region, the local bond susceptibility diverges at T=0. This shows the existence of degenerate bond spin excitation and implies quantum criticality and bond order formation when long range correlations are considered. The strong correlation between excitations on parallel neighboring bonds suggests bond singlet dimerization. The suppression of divergence for $n< \approx 0.78$ implies that tor these model parameters this is quantum critical point which separates the unconventional pseudogap region characterized by bond order from a conventional Fermi liquid.Comment: 5 pages, 5 figure

Financial innovation and corporate mergers

Consolidation and merger of corporations

A Maximum Entropy Method of Obtaining Thermodynamic Properties from Quantum Monte Carlo Simulations

We describe a novel method to obtain thermodynamic properties of quantum systems using Baysian Inference -- Maximum Entropy techniques. The method is applicable to energy values sampled at a discrete set of temperatures from Quantum Monte Carlo Simulations. The internal energy and the specific heat of the system are easily obtained as are errorbars on these quantities. The entropy and the free energy are also obtainable. No assumptions as to the specific functional form of the energy are made. The use of a priori information, such as a sum rule on the entropy, is built into the method. As a non-trivial example of the method, we obtain the specific heat of the three-dimensional Periodic Anderson Model.Comment: 8 pages, 3 figure

Sensor Technology using Fluorescent Dyes

This project is concerned with the application of fluorescent dye technology for leak detection in pulp and paper recovery boiler systems in order to avoid a smelt / water explosion. The dyes’ property to absorb light of short wavelength and emit light of a longer wavelength (fluoresce) is what makes them a quintessential candidate for the desired sensor technology. The projected benefits of this technology pertain to cost-effectiveness and safety of recovery boiler operations. For all purposes, the inert dye pyrenetetrasulfonic acid (PTSA) was used as a tracer agent. Multiple methods of experimental design were attempted to determine the reaction kinetics of the aforementioned dye. These methods involved exposing the dye to a specific temperature and monitoring its decomposition rate manually using a fluorometer. The dye was exposed to elevated temperature and pressure conditions in microwave reactors, such as Biotage and CEM Microwave. A design of experiments protocol was developed and executed, and the data collected was analyzed. It was established that PTSA decomposed on a 1st order reaction rate, and corresponding mathematical models were established using mass and energy balances. MATLAB simulations were developed and compared with actual experimental data conducted in a continuous stirred tanks reactor (CSTR) to simulate the real-time conditions of a leak environment. The data collected was also used to demonstrate the accuracy of the mathematical model. The leak detection system is based on steady-state conditions using the PTSA mass balance model as a reference point for any changes that might occur in the system. The decomposition rate of PTSA was monitored through careful recordings of a fluorometer. The decay rate analysis shows a decrease in the dye concentration in water with respect to time. The MATLAB simulation curve demonstrates the logarithmic relationship per the CSTR method at 150 °C and 200 °C. Further research and experimentation is required to understand the dynamics of these fluorescent dyes and their rate kinetics at elevated conditions to match the 10 MPa and 480 °C recovery boiler conditions. This innovative method of applying such world-class detection technology will ultimately mitigate risk by saving lives of employees in the industrial facility and facilitate the process of maximizing profit and minimizing costs associated with a shut-down in the case of a leak.https://scholarscompass.vcu.edu/capstone/1155/thumbnail.jp

Transport Properties of the Infinite Dimensional Hubbard Model

Results for the optical conductivity and resistivity of the Hubbard model in infinite spatial dimensions are presented. At half filling we observe a gradual crossover from a normal Fermi-liquid with a Drude peak at $\omega=0$ in the optical conductivity to an insulator as a function of $U$ for temperatures above the antiferromagnetic phase transition. When doped, the ``insulator'' becomes a Fermi-liquid with a corresponding temperature dependence of the optical conductivity and resistivity. We find a $T^2$-coefficient in the low temperature resistivity which suggests that the carriers in the system acquire a considerable mass-enhancement due to the strong local correlations. At high temperatures, a crossover into a semi-metallic regime takes place.Comment: 14 page

Improved Maximum Entropy Analysis with an Extended Search Space

The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.Comment: 18 pages, 6 figures, v3 includes several changes in text and figures, t.b.p. in Journal of Computational Physics, source code at http://www.scicode.org/ExtME

Optical conductivity of the infinite-dimensional Hubbard model

A Monte Carlo-maximum entropy calculation of the optical conductivity of the infinite-dimensional Hubbard model is presented. We show that the optical conductivity displays the anomalies found in the cuprate superconductors, including a Drude width which grows linearly with temperature, a Drude weight which grows linearly with doping, and a temperature and doping-dependent mid-IR peak. These anomalies arise as a consequence of the dynamical generation of a quasiparticle band at the Fermi energy as T -> 0, and are a generic property of the strongly correlated Hubbard model in all dimensions greater than one.Comment: 24 pages, revtex, including 5 figures compressed with uufile