Numerical studies on quantum phase transition of Anderson models.

Li, Ying Wai = 安德森模型下量子相變的數值研究 / 李盈慧.Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.Includes bibliographical references (leaves 69-72).Text in English; abstracts in English and Chinese.Li, Ying Wai = Andesen mo xing xia liang zi xiang bian de shu zhi yan jiu / Li, Yinghui.Chapter 1 --- Review on Anderson Models and Quantum Phase Transitions --- p.1Chapter 1.1 --- The Anderson Impurity Model --- p.1Chapter 1.2 --- The Periodic Anderson Model --- p.2Chapter 1.3 --- Quantum Phase Transitions (QPTs) --- p.3Chapter 1.4 --- Motivation of this project --- p.4Chapter 2 --- Studies on the Ground State Energy of Periodic Anderson Model --- p.7Chapter 2.1 --- Background --- p.7Chapter 2.2 --- Hamiltonian and Physical Meanings of Lattice Anderson Model --- p.8Chapter 2.2.1 --- The first term: -t ´iσ （c+̐ưσci+lσ + h.c.) --- p.8Chapter 2.2.2 --- The second term: Ef´iσ̐ưfiσ --- p.9Chapter 2.2.3 --- The third term: V ´ ̐ưσ (c+iσ̐ư̐ưσ + h.c.) --- p.9Chapter 2.2.4 --- The fourth term: U ̐ưσ´ nfitnfi↓ --- p.9Chapter 2.2.5 --- The whole Hamiltonian --- p.10Chapter 2.3 --- Non-Interacting Case of Lattice Anderson Model --- p.10Chapter 2.3.1 --- The Hamiltonian in momentum space --- p.11Chapter 2.3.2 --- The conduction band eK --- p.12Chapter 2.3.3 --- The band energies ±K --- p.12Chapter 2.3.4 --- The energy band gap Δ --- p.14Chapter 2.3.5 --- Green's functions at finite temperature --- p.14Chapter 2.4 --- Perturbation in U for symmetric model --- p.16Chapter 2.4.1 --- Previous Results --- p.16Chapter 2.4.2 --- Ground state energy at finite temperature by time-dependent perturbation theory --- p.18Chapter 3 --- Numerical Integration using Wang-Landau Sampling --- p.22Chapter 3.1 --- Background --- p.22Chapter 3.2 --- Wang-Landau integration --- p.25Chapter 3.2.1 --- Description of the method --- p.25Chapter 3.2.2 --- Correspondence between Wang-Landau sampling for physical systems and Wang-Landau integration --- p.27Chapter 3.3 --- Results --- p.28Chapter 3.3.1 --- Application to one- and two-dimensional test integrals . --- p.28Chapter 3.3.2 --- An example of a potential application: Perturbative calculation of the lattice Anderson model --- p.31Chapter 3.3.3 --- Discussion and summary --- p.35Chapter 4 --- Studies on QPT of Anderson Impurity Model by Quantum Entanglement --- p.38Chapter 4.1 --- Background --- p.38Chapter 4.2 --- Formalism --- p.39Chapter 4.2.1 --- Hamiltonian --- p.39Chapter 4.2.2 --- Conditions Used in Our Study --- p.40Chapter 4.2.3 --- Quantifying Quantum Entanglement: Entropy and Concurrence --- p.41Chapter 4.3 --- Numerical Results --- p.45Chapter 4.3.1 --- Method --- p.45Chapter 4.3.2 --- Finite Size Effects of the Ground State Energy --- p.46Chapter 4.3.3 --- Finite Size Effects of the Von Neumann Entropy --- p.49Chapter 4.3.4 --- Finite Size Effects of the Fermionic Concurrence --- p.53Chapter 4.4 --- Summary --- p.58Chapter 5 --- Fidelity in Critical Phenomena --- p.59Chapter 5.1 --- Background --- p.59Chapter 5.2 --- Ground State Fidelity and Dynamic Structure Factor --- p.60Chapter 5.3 --- Mixed-state fidelity and thermal phase transitions --- p.63Chapter 5.4 --- Summary --- p.64Chapter 6 --- Conclusion --- p.66Bibliography --- p.6

A histogram-free multicanonical Monte Carlo algorithm for the basis expansion of density of states

We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set and avoiding the explicit collection of a histogram. This practice also has the advantage of avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms.Comment: 8 pages, 6 figures. Paper accepted in the Platform for Advanced Scientific Computing Conference (PASC '17), June 26 to 28, 2017, Lugano, Switzerlan

A generic software framework for Wang-Landau type algorithms

The Wang-Landau (WL) algorithm is a stochastic algorithm designed to compute densities of states of a physical system. Is has also been recently used to perform challenging numerical integration in high-dimensional spaces. Using WL requires specifying the system handled, the proposal to explore the definition domain, and the measured against which one integrates. Additionally, several design options related to the learning rate must be provided. This work presents the first generic (C++) implementation providing all such ingredients. The versatility of the framework is illustrated with a variety of problems including the computation of density of states of physical systems and biomolecules, and the computation of high dimensional integrals. Along the way, we that integrating against a Boltzmann like measure to estimate DoS with respect to the Lebesgue measure can be beneficial. We anticipate that our implementation, available in the Structural Bioinformatics Library (http: //sbl.inria.fr), will leverage experiments on complex systems and contribute to unravel free energy calculations for (bio-)molecular systems