Recent developments in Quantum Monte-Carlo simulations with applications for cold gases

This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons, and spinful bosonic systems. For repulsive fermionic systems determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.Comment: 68 pages, 22 figures, review article; replaced with published versio

HUBO and QUBO models for Prime factorization

The security of the RSA cryptosystem is based on the difficulty of factoring a large number N into prime numbers p and q satisfying N=p*q . This paper presents a prime factoriaation method using D-Wave quantum computer that can threaten the RSA cryptosystem. The starting point for this method is very simple, representing two prime numbers as qubits. Then, set the difference between the product of two prime numbers expressed in qubits and N as a cost function, and find the solution when the cost function becomes the minimum. D-Wave's quantum annealer can find the minimum value of any quadratic problem. However, the cost function is to be a higher-order unconstrained optimiaation (HUBO) model because it contains the second or higher order terms. We used a hybrid solver and dimod package provided by -Wave Ocean software development kit (SDK) to solve the HUBO problem. We also successfully factoriaed 102,454,763 with 26 logical qubits. In addition, we factoriaed 1,000,070,001,221 using the range dependent Hamiltonian algorithm.Comment: 11 pag

Energetics and switching of quasi-uniform states in small ferromagnetic particles

We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size

Structural and magnetic characterization of nitrogen ion implanted stainless steel and CoCrMo alloys

Thesis (Master)--Izmir Institute of Technology, Physics, Izmir, 2014Includes bibliographical references (leaves: 80-83)Text in English; Abstract: Turkish and Englishxii, 83 leavesIon beam surface modification methods can be used to create hard and wear resistant surface layers with enhanced corrosion resistance on austenitic stainless steels (SS) and CoCr base alloys using nitrogen ions. This is mainly due to the formation of high N content phase, γN, at relatively low substrate temperatures from about 350 to 450 ºC. This surface layer is known as an expanded austenite layer. Different N contents and diffusion rates depending on grain orientations as well as anisotropic lattice expansion and high residual stresses are some peculiar properties associated with the formation of this phase. Another peculiar feature of the expanded austenite phase is related to its magnetic character. In this study, new data related to the magnetic nature of the expanded austenite layers on austenitic stainless steel (304 SS) and CoCrMo alloy by nitrogen plasma immersion ion implantation (PIII) are presented. Magnetic behaviour, nitrogen distribution, implanted layer phases, surface topography, and surface hardness were studied with a combination of experimental techniques involving magnetic force microscopy, SIMS, XRD, SEM, AFM and nanoindentation method. The experimental analyses indicate that the low temperature samples clearly show the formation of the expanded austenite phase, while the decomposition of this metastable phase into CrN precipitates occurs at higher temperatures. As a function of the processing temperature, phase evolution stage for both alloys follows the same trend: (1) initial stage of the expanded phase, γN, formation; (2) its full development, and (3) its decomposition into CrN precipitates and the Cr-depleted matrix, fcc γ-(Co,Mo) for CoCrMo and bcc α-(Fe,Ni) for 304 SS. MFM imaging reveals distinct, stripe-like ferromagnetic domains for the fully developed expanded austenite layers both on 304 SS and CoCrMo alloys. Weak domain structures are observed for the CoCrMo samples treated at low and high processing temperatures. The images also provide strong evidence for grain orientation dependence of magnetic properties. The ferromagnetic state for the γN phase observed here is mainly linked to large lattice expansions due to high N content

Scalable Emulation of Sign-Problem−-Free Hamiltonians with Room Temperature p-bits

The growing field of quantum computing is based on the concept of a q-bit which is a delicate superposition of 0 and 1, requiring cryogenic temperatures for its physical realization along with challenging coherent coupling techniques for entangling them. By contrast, a probabilistic bit or a p-bit is a robust classical entity that fluctuates between 0 and 1, and can be implemented at room temperature using present-day technology. Here, we show that a probabilistic coprocessor built out of room temperature p-bits can be used to accelerate simulations of a special class of quantum many-body systems that are sign-problem$-$free or stoquastic, leveraging the well-known Suzuki-Trotter decomposition that maps a $d$-dimensional quantum many body Hamiltonian to a $d$+1-dimensional classical Hamiltonian. This mapping allows an efficient emulation of a quantum system by classical computers and is commonly used in software to perform Quantum Monte Carlo (QMC) algorithms. By contrast, we show that a compact, embedded MTJ-based coprocessor can serve as a highly efficient hardware-accelerator for such QMC algorithms providing several orders of magnitude improvement in speed compared to optimized CPU implementations. Using realistic device-level SPICE simulations we demonstrate that the correct quantum correlations can be obtained using a classical p-circuit built with existing technology and operating at room temperature. The proposed coprocessor can serve as a tool to study stoquastic quantum many-body systems, overcoming challenges associated with physical quantum annealers.Comment: Fixed minor typos and expanded Appendi

The Study of Transition Metal Oxides using Dynamical Mean Field Theory

In this thesis, we study strong electron correlation in transition metal oxides. In the systems with large Coulomb interaction, especially the on-site interaction, electrons are much more correlated and cannot be described using traditional one-electron picture, thus the name "strongly correlated systems". With strong correlation, there exists a variety of interesting phenomena in these systems that attract long-standing interests from both theorists and experimentalists. Transition metal oxides (TMOs) play a central role in strongly correlated systems, exhibiting many exotic phenomena. The fabrication of heterostructures of transition metal oxides opens many possible directions to control bulk properties of TMOs as well as revealing physical phases not observed in bulk systems. Dynamical mean-field theory (DMFT) emerges as a successful numerical method to treat the strong correlation. The combination of density functional and dynamical mean-field theory (DFT+DMFT) is a prospective ab initio approach for studying realistic strongly correlated materials. We use DMFT as well as DFT+DMFT methods as main approaches to study the strong correlation in these materials. We focus on some aspects and properties of TMOs in this work. We study the magnetic properties in bulk TMOs and the possibility of enhancing the magnetic order in TMO heterostructures. We work on the metallic/insulating behaviors of these systems to understand how the metal-insulator transition depends on the intrinsic parameters of materials. We also investigate the effect of a charged impurity to the neighborhood of a correlated material, which can be applied, for example, to the study of muon spin relaxation measurements in high-Tc superconductors

Computational Physics on Graphics Processing Units

The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing on classical molecular dynamics, and on quantum simulations for electronic structure calculations using the density functional theory, wave function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012, Helsinki, Finland, June 10-13, 201