Janus II: a new generation application-driven computer for spin-system simulations

This paper describes the architecture, the development and the implementation of Janus II, a new generation application-driven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of computational physics is a recognized grand challenge of high-performance computing: the resources necessary to study in detail theoretical models that can make contact with experimental data are by far beyond those available using commodity computer systems. On the other hand, several specific features of the associated algorithms suggest that unconventional computer architectures, which can be implemented with available electronics technologies, may lead to order of magnitude increases in performance, reducing to acceptable values on human scales the time needed to carry out simulation campaigns that would take centuries on commercially available machines. Janus II is one such machine, recently developed and commissioned, that builds upon and improves on the successful JANUS machine, which has been used for physics since 2008 and is still in operation today. This paper describes in detail the motivations behind the project, the computational requirements, the architecture and the implementation of this new machine and compares its expected performances with those of currently available commercial systems.Comment: 28 pages, 6 figure

Highly optimized simulations on single- and multi-GPU systems of 3D Ising spin glass

We present a highly optimized implementation of a Monte Carlo (MC) simulator for the three-dimensional Ising spin-glass model with bimodal disorder, i.e., the 3D Edwards-Anderson model running on CUDA enabled GPUs. Multi-GPU systems exchange data by means of the Message Passing Interface (MPI). The chosen MC dynamics is the classic Metropolis one, which is purely dissipative, since the aim was the study of the critical off-equilibrium relaxation of the system. We focused on the following issues: i) the implementation of efficient access patterns for nearest neighbours in a cubic stencil and for lagged-Fibonacci-like pseudo-Random Numbers Generators (PRNGs); ii) a novel implementation of the asynchronous multispin-coding Metropolis MC step allowing to store one spin per bit and iii) a multi-GPU version based on a combination of MPI and CUDA streams. We highlight how cubic stencils and PRNGs are two subjects of very general interest because of their widespread use in many simulation codes. Our code best performances ~3 and ~5 psFlip on a GTX Titan with our implementations of the MINSTD and MT19937 respectively.Comment: 39 pages, 13 figure

Performance potential for simulating spin models on GPU

Graphics processing units (GPUs) are recently being used to an increasing degree for general computational purposes. This development is motivated by their theoretical peak performance, which significantly exceeds that of broadly available CPUs. For practical purposes, however, it is far from clear how much of this theoretical performance can be realized in actual scientific applications. As is discussed here for the case of studying classical spin models of statistical mechanics by Monte Carlo simulations, only an explicit tailoring of the involved algorithms to the specific architecture under consideration allows to harvest the computational power of GPU systems. A number of examples, ranging from Metropolis simulations of ferromagnetic Ising models, over continuous Heisenberg and disordered spin-glass systems to parallel-tempering simulations are discussed. Significant speed-ups by factors of up to 1000 compared to serial CPU code as well as previous GPU implementations are observed.Comment: 28 pages, 15 figures, 2 tables, version as publishe

Lattice gauge theories simulations in the quantum information era

The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analyzing the symmetry properties of Hamiltonian and states: the most striking example are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realization of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.Comment: Pedagogical review article. Originally submitted to Contemporary Physics, the final version will appear soon on the on-line version of the journal. 34 page

Study of Condensed Matter Systems with Monte Carlo Simulation on Heterogeneous Computing Systems

We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field. We employ an indicator composed of a ratio of susceptibilities at finite momenta, which was recently proposed to avoid the difficulties of a zero momentum quantity, for capturing the spin glass phase transition. Unfortunately, this new indicator is fairly noisy, so a large pool of samples at low temperature and small external field are needed to generate results with a sufficiently small statistical error for analysis. We thus implement the Monte Carlo method using graphics processing units to drastically speed up the simulation. We confirm previous findings that conventional indicators for the spin glass transition, including the Binder ratio and the correlation length do not show any indication of a transition for rather low temperatures. However, the ratio of spin glass susceptibilities does show crossing behavior, albeit a systematic analysis is beyond the reach of the present data. This reveals the difficulty with current numerical methods and computing capability in studying this problem. One of the fundamental challenges of theoretical condensed matter physics is the accurate solution of quantum impurity models. By taking expansion in the hybridization about an exactly solved local limit, one can formulate a quantum impurity solver. We implement the hybridization expansion quantum impurity solver on Intel Xeon Phi accelerators, and aim to apply this approach on the Dynamic Hubbard Models

Rugged free-energy landscapes in disordered spin systems

This thesis is an attempt to provide a new outlook on complex systems, as well as some physical answers for certain models, taking a computational approach. We have focused on disordered systems, addressing two traditional problems in three spatial dimensions: the Edwards-Anderson spin glass and the Diluted Antiferromagnet in a Field (the physical realisation of the random-field Ising model). These systems have been studied by means of large-scale Monte Carlo simulations, exploiting a variety of platforms, which include the Janus special-purpose supercomputer. Two main themes are explored throughout: a) the relationship between the (experimentally unreachable) equilibrium phase and the non-equilibrium evolution and b) the computation and efficient treatment of rugged free-energy landscapes. We perform a thorough study of the low-temperature phase of the D=3 Edwards-Anderson spin glass, where we establish a time-length dictionary and a finite-time scaling formalism to link, in a quantitative way, the experimental non-equilibrium regime and the finite-size equilibrium phase. At the experimentally relevant scales, the replica symmetry breaking theory emerges as the appropriate theoretical picture. We also introduce Tethered Monte Carlo, a general strategy for the study of systems with rugged free-energy landscapes. This formalism provides a general method to guide the exploration of the configuration space by constraining one or more reaction coordinates. From these tethered simulations, the Helmholtz potential associated to the reaction coordinates is reconstructed, yielding all the information about the system. We use this method to provide a comprehensive picture of the critical behaviour in the Diluted Antiferromagnet in a Field.Comment: PhD Thesis. Defended at the Universidad Complutense de Madrid on October 21, 201

Tree tensor networks for high-dimensional quantum systems and beyond

This thesis presents the development of a numerical simulation technique, the Tree Tensor Network, aiming to overcome current limitations in the simulation of two- and higher-dimensional quantum many-body systems. The development and application of methods based on Tensor Networks (TNs) for such systems are one of the most relevant challenges of the current decade with the potential to promote research and technologies in a broad range of fields ranging from condensed matter physics, high-energy physics, and quantum chemistry to quantum computation and quantum simulation. The particular challenge for TNs is the combination of accuracy and scalability which to date are only met for one-dimensional systems by other established TN techniques. This thesis first describes the interdisciplinary field of TN by combining mathematical modelling, computational science, and quantum information before it illustrates the limitations of standard TN techniques in higher-dimensional cases. Following a description of the newly developed Tree Tensor Network (TTN), the thesis then presents its application to study a lattice gauge theory approximating the low-energy behaviour of quantum electrodynamics, demonstrating the successful applicability of TTNs for high-dimensional gauge theories. Subsequently, a novel TN is introduced augmenting the TTN for efficient simulations of high-dimensional systems. Along the way, the TTN is applied to problems from various fields ranging from low-energy to high-energy up to medical physics.In dieser Arbeit wird die Entwicklung einer numerischen Simulationstechnik, dem Tree Tensor Network (TTN), vorgestellt, die darauf abzielt, die derzeitigen Limitationen bei der Simulation von zwei- und höherdimensionalen Quanten-Vielteilchensystemen zu überwinden. Die Weiterentwicklung von auf Tensor-Netzwerken (TN) basierenden Methoden für solche Systeme ist eine der aktuellsten und relevantesten Herausforderungen. Sie birgt das Potential, Forschung und Technologien in einem breiten Spektrum zu fördern, welches sich von der Physik der kondensierten Materie, der Hochenergiephysik und der Quantenchemie bis hin zur Quantenberechnung und Quantensimulation erstreckt. Die besondere Herausforderung für TN ist die Kombination von Genauigkeit und Skalierbarkeit, die bisher nur für eindimensionale Systeme erfüllt wird. Diese Arbeit beschreibt zunächst das interdisziplinäre Gebiet der TN als eine Kombination von mathematischer Modellierung, Computational Science und Quanteninformation, um dann die Grenzen der Standard-TN-Techniken in höherdimensionalen Fällen aufzuzeigen. Nach einer Beschreibung des neu entwickelten TTN stellt die Arbeit dessen Anwendung zur Untersuchung einer Gittereichtheorie vor, die das Niederenergieverhalten der Quantenelektrodynamik approximiert und somit die erfolgreiche Anwendbarkeit von TTNs für hochdimensionale Eichtheorien demonstriert. Anschließend wird ein neuartiges TN eingeführt, welches das TTN für effiziente Simulationen hochdimensionaler Systeme erweitert. Zusätzlich wird das TTN auf diverse Probleme angewandt, die von Niederenergie- über Hochenergie- bis hin zur medizinischen Physik reichen

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Electronic coupling calculations for modelling charge transport in organic semiconductors

Charge transport in organic semiconductors (OSCs) depends on a number of molecular properties, one of which is the electronic coupling matrix element for charge transfer between the molecules forming the material. They are the off-diagonal elements of the electronic Hamiltonian in the charge-localised (or diabatic) basis. The focus of this work is on the development of a method for a fast calculation of these matrix elements for OSCs. After addressing the different methods of their calculation, I present a program to estimate the off-diagonal elements of the Hamiltonian with a fast yet accurate semi-empirical method. This model approximates the off-diagonal elements of the Hamiltonian to be proportional to the overlap between the orbitals of the molecules, which are projected onto a very small basis set. The analytical results are in a reasonable agreement with accurate ab initio and fragment orbital DFT calculations and the speed-up is up to six orders of magnitude compared to DFT calculations. Following on from this, the analytic overlap method was implemented in two programs for charge carrier propagation, one based on Kinetic Monte Carlo simulation of charge carrier hopping (presented here), the other on surface hopping non-adiabatic molecular dynamics. I also show that the analytic overlap method can be used to estimate non-adiabatic coupling vectors very efficiently, which is an important quantity in surface hopping simulations