DOCSLIB.ORG

Numerical Quenches of Disorder in the Bose-Hubbard Model

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Numerical Quenches of Disorder in the Bose-Hubbard Model Universidade Estadual de Campinas Instituto de Física Gleb Wataghin Bruno Ricardi de Abreu Quenches numéricos de desordem no modelo Bose-Hubbard Numerical quenches of disorder in the Bose-Hubbard model CAMPINAS 2018 Bruno Ricardi de Abreu Numerical quenches of disorder in the Bose-Hubbard model Quenches numéricos de desordem no modelo Bose-Hubbard Tese apresentada ao Instituto de Física Gleb Wa- taghin da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obten- ção do título de Doutor em Ciências. Thesis presented to the Institute of Physics Gleb Wataghin of the University of Campinas in par- tial fulfillment of the requirements for the degree of Doctor in Sciences. Orientador: Silvio Antonio Sachetto Vitiello Este exemplar corresponde à versão final da tese defendida pelo aluno Bruno Ricardi de Abreu, e orientada pelo Prof. Dr. Silvio An- tonio Sachetto Vitiello. Campinas 2018 Agência(s) de fomento e nº(s) de processo(s): CNPq, 141252/2014-0; CNPq, 232682/2014-3 ORCID: ttps://orcid.org/0000-0002-9067-779X Ficha catalográfica Universidade Estadual de Campinas Biblioteca do Instituto de Física Gleb Wataghin Lucimeire de Oliveira Silva da Rocha - CRB 8/9174 Abreu, Bruno Ricardi de, 1990- Ab86n AbrNumerical quenches of disorder in the Bose-Hubbard model / Bruno Ricardi de Abreu. – Campinas, SP : [s.n.], 2018. AbrOrientador: SIlvio Antonio Sachetto Vitiello. AbrTese (doutorado) – Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin. Abr1. Superfluidez. 2. Bose-Hubbard, Modelo de. 3. Monte Carlo quântico, Método de. 4. Sistemas desordenados. 5. Átomos ultrafrios. I. Vitiello, Silvio Antonio Sachetto, 1950-. II. Universidade Estadual de Campinas. Instituto de Física Gleb Wataghin. III. Título. Informações para Biblioteca Digital Título em outro idioma: Quenches numéricos de desordem no modelo Bose-Hubbard Palavras-chave em inglês: Superfluidity Bose-Hubbard model Quantum Monte Carlo method Disordered systems Ultracold atoms Área de concentração: Física Titulação: Doutor em Ciências Banca examinadora: Silvio Antonio Sachetto Vitiello Ricardo Luis Doretto Marcos Cesar de Oliveira Raimundo Rocha dos Santos José Abel Hoyos Neto Data de defesa: 08-08-2018 Programa de Pós-Graduação: Física Powered by TCPDF (www.tcpdf.org) MEMBROS DA COMISSÃO JULGADORA DA TESE DE DOUTORADO DE BRUNO RICARDI DE ABREU RA: 80858 APRESENTADA E APROVADA AO INSTITUTO DE FÍSICA “GLEB WATAGHIN”, DA UNIVERSIDADE ESTADUAL DE CAMPINAS, EM 08/08/2018. COMISSÃO JULGADORA: - Prof. Dr. Silvio Antonio Sachetto Vitiello - (Orientador) - IFGW/UNICAMP - Prof. Dr. Ricardo Luis Doretto - IFGW/UNICAMP - Prof. Dr. Marcos Cesar de Oliveira - IFGW/UNICAMP - Prof. Dr. Raimundo Rocha dos Santos - INSTITUTO DE FÍSICA - UFRJ - Prof. Dr. José Abel Hoyos Neto - INSTITUTO DE FÍSICA/SÃO CARLOS A Ata de Defesa, assinada pelos membros da Comissão Examinadora, consta no processo de vida acadêmica do aluno. CAMPINAS 2018 Acknowledgements My entire career as a physics student and, in particular, the work that is presented in this dissertation could not be possibly made without the unconditional love and support that I have always received from my family. I feel like just thanking them on these lines does not even fairly compensate for the most elemental source of motivation that they represent to me. Even so, if not by other means, I express here my gratefulness for having them in my life. It is an extraordinarily comforting pleasure to be sure that they will always be by side no matter the possible different courses that my life would take as a consequence of my choices. Just as important as them for the construction of my career as a physicist, the development of this work, and for my formation as a citizen and human being during my time as a student at Unicamp is my long-term advisor Silvio Vitiello. Along our journey he has consistently been aware of my feelings, tempering my thoughts when they were too fast and confusing, hastening my ideas when I was moving too slow and wisely advising me in a number of situations of life with distinguished discernment and sagacity. I am deeply thankful for his unrestricted patience and perseverance during this period. I am also very gratified for people that work at IFGW/Unicamp and made this project possible. From faculty, with highly skilled professors that taught me physics on the finest level, to staff that provided fundamental support such as access to scientific books and articles through the library (BIF), scheduling of classrooms for presentations whenever needed and so many other things, including hot, good coffee and snacks. I am completely sure that they made academic lifehere a lot easier for me. I must also recognize that this research used the computing resources and assistance of the John David Rogers Computing Center (CCJDR) in IFGW, whose staff has been extremelly supportive as well. Part of this work was made in the United States, more specifically at the University of Illinois at Urbana-Champaing (UIUC), Institute for Condensed Matter Theory (ICMT), where I have been a visiting scholar with Professor David Ceperley. He has demonstrated that, much more than the extraordinary scientist that his career grants, he is an excellent human being. He helped me by being kind and prestative, keeping my hopes alive during what was, beyond any doubts, the hardest piece of my life so far. I am deeply grateful for his support, which of course extended to academic and research life. During this period I also met Ushnish Ray, an excepetionally talented scientist that has guided me through the subtleties of the subjects and methods that were used throughout this work. I am thankful for his patience, consideration and collaboration. Last, but not least, I shall say that I have been exceedingly lucky in finding new friends and keeping old ones during these years, both in Brasil and in the United States. Their friendship is priceless and makes life worth living. During my time in the US, I met my beloved Kinsey who has, since then, sweetened my life with unequivocal love, support and kindness, softening my heart whenever my hard thoughts were overcoming my feelings. I am thankful for financial support from the Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq under grants No. 141242/2014-0 and No. 232682/2014-3 that concern both regular doctorate scholarship and the Science Without Borders program. Resumo Neste trabalho as propriedades das fases superfluida (SF) e vidro de Bose (BG) do modelo Bose-Hubbard desordenado em três dimensões são investigadas usando simulações de Monte Carlo quântico. O diagrama de fases é construído utilizando desordem Gaussiana nas energias de ocu- pação, e dois tipos adicionais de distribuição, exponencial e uniforme, são estudados com respeito às suas influências quantitativas e qualitativas no estabelecimento do super-fluxo que caracteriza o estado superfluido. A estatística de observáveis do sistema pertinente a distribuições depro- babilidade sobre o ensemble de desordem são estudadas para diversos valores de interação entre átomos e tamanhos da rede, onde fortes efeitos de tamanho são observados. Estes efeitos estão relacionados ao mecanismo que dirige a transição SF-BG e corroboram o entendimento do caráter percolativo da transição. Apesar disso, ambos os parâmetros de ordem, a fração de superfluido e a compressibilidade, permanecem auto-promediantes por toda fase superfluida. Nos arredores do contorno SF-BG, efeitos de tamanho são dominantes mais ainda sugerem que a auto-promediação persiste. Estes resultados são relevantes para experimentos com gases atômicos ultrafrios onde um procedimento sistemático de mediação sobre realizações de desordem não é tipicamente possível, e também para cálculos numéricos que precisam necessariamente considerar efeitos de tamanho quando o sistema apresenta pequenas quantidades de superfluido. Palavras-chave: superfluidez, Monte Carlo quântico, modelo de Bose-Hubbard, desordem, vi- dro de Bose, percolação, auto-promediação, modelo de Bose-Hubbard desordenado, gases atômicos ultrafrios Abstract In this work the properties of the superfluid (SF) and Bose-glass (BG) phases in the three- dimensional disordered Bose-Hubbard model are investigated using Quantum Monte-Carlo simu- lations. The phase diagram is generated using Gaussian disorder on the on-site potential, and two additional types of distributions, namely exponential and uniform, are studied regarding both their qualitative and quantitative influence on the establishment of the superflow that characterizes the superfluid state. Statistics pertaining to probability distributions of observables over the disorder ensemble are studied for a range of interaction strengths and system sizes, where strong finite-size effects are observed. These effects are related to the mechanism that drives the SF-BG transition and corroborates the understanding of the percolation character of the transition. Despite this, both order parameters, the superfluid fraction and compressibility, remain self-averaging through- out the superfluid phase. Close to the superfluid-Bose-glass phase boundary, finite-size effects dominate but still suggest that self-averaging holds. These results are pertinent to experiments with ultracold atomic gases where a systematic disorder averaging procedure is typically not pos- sible, and also to numerical calculations that must necessarily address finite-size effects when the system exhibits small amounts of superfluid. Keywords: superfluidity, Quantum Monte
Load more

Recommended publications
  • Annual-Report-BW Ceperley
    Annual Report for Blue Waters Allocation January 2016 Project Information o Title: Quantum Simulations o PI: David Ceperley (Blue Waters professor), Department of Physics, University of Illinois Urbana-Champaign o Norm Tubman University of Illinois Urbana-Champaign (former postdoc), Carlo Pierleoni (Rome, Italy), Markus Holzmann(Grenoble, France) o Corresponding author: David Ceperley, [email protected] Executive summary (150 words) Much of our research on Blue Waters is related to the “Materials Genome Initiative,” the federally supported cross-agency program to develop computational tools to design materials. We employ Quantum Monte Carlo calculations that provide nearly exact information on quantum many-body systems and are also able to use Blue Waters effectively. This is the most accurate general method capable of treating electron correlation, thus it needs to be in the kernel of any materials design initiative. Ceperley’s group has a number of funded and proposed projects to use Blue Waters as discussed below. In the past year, we have been running calculations for dense hydrogen in order to make predictions that can be tested experimentally. We have also been testing a new method that can be used to solve the fermion sign problem and to find dynamical properties of quantum systems. Description of research activities and results During the past year, the following 4 grants of which Ceperley is a PI or CoPI, and that involve Blue Waters usage, have had their funding renewed. Access to Blue Waters is crucial for success of these projects. • “Warm dense matter”DE-NA0001789. Computation of properties of hydrogen and helium under extreme conditions of temperature and pressure.
    [Show full text]
  • The Early Years of Quantum Monte Carlo (1): the Ground State
    The Early Years of Quantum Monte Carlo (1): the Ground State Michel Mareschal1,2, Physics Department, ULB , Bruxelles, Belgium Introduction In this article we shall relate the history of the implementation of the quantum many-body problem on computers, and, more precisely, the usage of random numbers to that effect, known as the Quantum Monte Carlo method. The probabilistic nature of quantum mechanics should have made it very natural to rely on the usage of (pseudo-) random numbers to solve problems in quantum mechanics, whenever an analytical solution is out of range. And indeed, very rapidly after the appearance of electronic machines in the late forties, several suggestions were made by the leading scientists of the time , - like Fermi, Von Neumann, Ulam, Feynman,..etc- which would reduce the solution of the Schrödinger equation to a stochastic or statistical problem which , in turn, could be amenable to a direct modelling on a computer. More than 70 years have now passed and it has been witnessed that, despite an enormous increase of the computing power available, quantum Monte Carlo has needed a long time and much technical progresses to succeed while numerical quantum dynamics mostly remains out of range at the present time. Using traditional methods for the implementation of quantum mechanics on computers has often proven inefficient, so that new algorithms needed to be developed. This is very much in contrast with what happened for classical systems. At the end of the fifties, the two main methods of classical molecular simulation, Monte Carlo and Molecular Dynamics, had been invented and an impressively rapid development was going to take place in the following years: this has been described in previous works [Mareschal,2018] [Battimelli,2018].
    [Show full text]
  • The Early Years of Quantum Monte Carlo (2): Finite- Temperature Simulations
    The Early Years of Quantum Monte Carlo (2): Finite- Temperature Simulations Michel Mareschal1,2, Physics Department, ULB , Bruxelles, Belgium Introduction This is the second part of the historical survey of the development of the use of random numbers to solve quantum mechanical problems in computational physics and chemistry. In the first part, noted as QMC1, we reported on the development of various methods which allowed to project trial wave functions onto the ground state of a many-body system. The generic name for all those techniques is Projection Monte Carlo: they are also known by more explicit names like Variational Monte Carlo (VMC), Green Function Monte Carlo (GFMC) or Diffusion Monte Carlo (DMC). Their different names obviously refer to the peculiar technique used but they share the common feature of solving a quantum many-body problem at zero temperature, i.e. computing the ground state wave function. In this second part, we will report on the technique known as Path Integral Monte Carlo (PIMC) and which extends Quantum Monte Carlo to problems with finite (i.e. non-zero) temperature. The technique is based on Feynman’s theory of liquid Helium and in particular his qualitative explanation of superfluidity [Feynman,1953]. To elaborate his theory, Feynman used a formalism he had himself developed a few years earlier: the space-time approach to quantum mechanics [Feynman,1948] was based on his thesis work made at Princeton under John Wheeler before joining the Manhattan’s project. Feynman’s Path Integral formalism can be cast into a form well adapted for computer simulation. In particular it transforms propagators in imaginary time into Boltzmann weight factors, allowing the use of Monte Carlo sampling.
    [Show full text]
  • Path Integrals Calculations of Helium Droplets
    Imaginary Time Path Integral Calculations of Supersolid Helium David Ceperley Dept. of Physics and NCSA University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA In 1953 Feynman, introduced imaginary-time path integrals to understand superfluid 4He. Path integrals are an exact "isomorphism" between quantum systems and the classical statistical mechanics of ring "polymers" allowing one to understand Bose condensation from the point of view of classical statistical mechanics and to calculate many of its properties. Bose symmetry of the wave function implies that the polymers are allowed to “cross-link'' or exchange. Superfluidity (coupling to the boundaries) is proportional to the mean squared flux of polymers through a surface. Bose condensation is equivalent to the delocalization of the end-end distance of a cut polymer. We have developed specialized simulation methods (Path Integral Monte Carlo) based on the Metropolis Monte Carlo method, to simulate boson systems[1]. Andreev, Lifshitz, Chester, and Leggett suggested in about 1970 that a quantum crystal such as bulk helium-4 under pressure might show both crystallinity and superfluid behavior. Experiments by Kim and Chan within the last two years have found indications for such a supersolid phase. The theoretical explanation of superflow in a crystal assumed vacancies, however, they have not been seen experimentally and computer simulations do not find stable vacancies. The path integral picture allows one to address the question[2] of whether a highly fluctuating quantum crystal is “insulating” or “metallic”. We and others have done Path Integral Monte Carlo calculations of exchange frequencies[3], superfluid density and the condensate fraction[4].
    [Show full text]
  • Quantum Phase Transition from a Super¯Uid to a Mott Insulator in a Gas of Ultracold Atoms
    articles Quantum phase transition from a super¯uid to a Mott insulator in a gas of ultracold atoms Markus Greiner*, Olaf Mandel*, Tilman Esslinger², Theodor W. HaÈnsch* & Immanuel Bloch* * Sektion Physik, Ludwig-Maximilians-UniversitaÈt, Schellingstrasse 4/III, D-80799 Munich, Germany, and Max-Planck-Institut fuÈr Quantenoptik, D-85748 Garching, Germany ² Quantenelektronik, ETH ZuÈrich, 8093 Zurich, Switzerland ............................................................................................................................................................................................................................................................................ For a system at a temperature of absolute zero, all thermal ¯uctuations are frozen out, while quantum ¯uctuations prevail. These microscopic quantum ¯uctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. Here we observe such a quantum phase transition in a Bose±Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential depth of the lattice is increased, a transition is observed from a super¯uid to a Mott insulator phase. In the super¯uid phase, each atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice; this phase is characterized by a gap in the excitation spectrum. We can induce reversible changes between the two ground states of the system. A physical system that crosses the boundary between two phases (here between kinetic and interaction energy) is fundamental to changes its properties in a fundamental way. It may, for example, quantum phase transitions4 and inherently different from normal melt or freeze.
    [Show full text]
  • Variational Density Matrix Method for Warm Condensed Matter And
    Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen Burkhard Militzera) and E. L. Pollockb) a)Department of Physics University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 b)Physics Department, Lawrence Livermore National Laboratory, University of California, Livermore, California 94550 (August 8, 2018) A new variational principle for optimizing thermal density matrices is intro- duced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by Gaus- sians with the mean, width and amplitude as variational parameters. The method is illustrated for the particle in an external field problem, the hydrogen molecule and dense hydrogen where the molecular, the dissociated and the plasma regime are described. Structural and thermodynamic properties (energy, equation of state and shock Hugoniot) are presented. I. INTRODUCTION Considerable effort has been devoted to systems where finite temperature ions (treated either classically or quantum mechanically by path integral methods) are coupled to degenerate electrons on the Born-Oppenheimer surface. In contrast, the theory for similar systems with non-degenerate electrons (T a significant fraction of TF ermi) is relatively underdeveloped except at the extreme high T limit where Thomas-Fermi and similar theories apply. In this paper we present a computational approach for systems with non-degenerate electrons analogous to the methods used for ground state many body computations. Although an oversimplification, we may usefully view the ground state computations as consisting of three levels of increasing accuracy [1]. At the first level, the ground state wave function consists of determinants, for both spin species, of single particle orbitals often taken from local density functional theory Φ1(r1) ..
    [Show full text]
  • Multiparticle Interactions for Ultracold Atoms in Optical Tweezers: Cyclic Ring-Exchange Terms
    Multiparticle interactions for ultracold atoms in optical tweezers: Cyclic ring-exchange terms Annabelle Bohrdt,1, 2, ∗ Ahmed Omran,3, ∗ Eugene Demler,3 Snir Gazit,4 and Fabian Grusdt5, 2, 1, y 1Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany 2Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 M¨nchen,Germany 3Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 4Racah Institute of Physics and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 91904, Israel 5Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universit¨atM¨unchen,Theresienstr. 37, M¨unchenD-80333, Germany (Dated: October 2, 2019) Dominant multi-particle interactions can give rise to exotic physical phases with anyonic excita- tions and phase transitions without local order parameters. In spin systems with a global SU(N) symmetry, cyclic ring-exchange couplings constitute the first higher-order interaction in this class. In this letter we propose a protocol how SU(N) invariant multi-body interactions can be imple- mented in optical tweezer arrays. We utilize the flexibility to re-arrange the tweezer configuration on time scales short compared to the typical lifetimes, in combination with strong non-local Rydberg interactions. As a specific example we demonstrate how a chiral cyclic ring-exchange Hamiltonian can be implemented in a two-leg ladder geometry. We study its phase diagram using DMRG sim- ulations and identify phases with dominant vector chirality, a ferromagnet, and an emergent spin-1 Haldane phase. We also discuss how the proposed protocol can be utilized to implement the strongly frustrated J − Q model, a candidate for hosting a deconfined quantum critical point.
    [Show full text]
  • 2014 Blue Waters Update
    2014 Blue Waters Update Bill Kramer Blue Waters Director Announcements • Today, Ed Seidel has invited the PIs to lunch in the Alma Mater Room. • The PI's have blue tickets in the back of their badges. • We will take a group photo of all attendees at the first break. • #BWsymp2014 for another chance BW Symposium - May 2014 2 Joint Dinner at Memorial Stadium – Tonight Joint with the Private Sector Program Workshop Attendees BW Symposium - May 2014 3 SETAC NSF PRAC • Paul Woodward, Physics and Astrophysics, University of Minnesota • Tom Cheatham, Chemistry, University of Utah • Patrick Reed, Civil and Environmental Engineering – Systems Optimization, Cornell • Klaus Schulten, Physics and Molecular Dynamic, University of Illinois Urbana-Champaign • David Ceperley, Physics and Material Science, University of Illinois Urbana-Champaign • Tiziana Di Matteo, Physics and Cosmology, Carnegie Mellon University • Dave Randall, Atmospheric Sciences and Climate Colorado State University GLCPC Chair • Joe Paris, Academic & Research Technologies in Information Technology, Northwestern University (Chair for 2013/2014, followed by Jorge Vinals, Structural Mechanics and Biophysics, University of Minnesota, Chair for 2014/2015) University of Illinois at Urbana-Champaign Allocation Chair • Athol Kemball, Atmospheric Sciences, University of Illinois at Urbana-Champaign Industry • Rick Authur, General Electric Global Research, Computer and Software Engineering BW Symposium - May 2014 4 Blue Waters Fellows • 6 Awards (so far) • Substantial Stipend + Blue Waters allocations • 10 other very deserving nominees are being offered Blue Waters allocations • Kenza Arraki, New Mexico State University • Jon Calhoun, University of Illinois at Urbana-Champaign • Sara Kokkila, Stanford University, • Edwin Mathews, University of Notre Dame • Ariana Minot, Harvard University • Derek Vigil-Fowler, University of California, Berkeley BW Symposium - May 2014 5 Blue Waters Usage 2/11/14 – Largest 10 Jobs-Torus View Each dot is a Gemini router and represents 64 AMD integer cores.
    [Show full text]
  • Fermi Condensates
    ��� ���� � �� ������ �� ������� ����� ����������� ��� ��������������� ��������� �� ���� ������ ����� �� � �� ���� ���� ����� ����������� ��������� ��� ������ ������� ���������� �� �������� �� �������� ��� ICTP SCHOOL ON QUANTUM PHASE TRANSITIONS AND NON-EQUILIBRIUM PHENOMENA IN COLD ATOMIC GASES 2005 Fermi condensates Markus Greiner JILA, Group of D. Jin; Coworkers: C. Regal and J. Stewart NIST and the University of Colorado, Boulder Highly controlled many-body quantum systems Weakly interacting Bose gases: Coherence, superfluid flow, vortices … Strongly correlated Bose systems: Superfluid to Mott insulator transition Fermionic superfluidity: BCS-BEC crossover physics • Condensed matter physics studied with an atomic physics system Outline: • Fermionic superfluidity; The tools: trapping, cooling, probing; • Controlling interactions; Molecular Bose-Einstein condensate; Fermi condensate: Generalized Cooper pairs in the BCS-BEC crossover; • Probing the fermion momentum distribution • Detecting atom-atom correlations via atom shot noise; Bosons Fermions integer spin half-integer spin <1,2 = <2,1 <1,2 = -<2,1 Æ Bosonic Æ Pauli exclusion enhancement principle EF= kbTF spin n spin p 1995: Bose-Einstein condensation 1999: Fermi sea of atoms e.g. 87Rb, 23Na, H, 39K … 40K, 6Li photons, liquid 4He electrons, protons, neutrons Pairing and Superfluidity Æ Spin is additive: Fermions can pair up and form effective bosons: <(1,…,N) =  [ I(1,2) I(3,4) … I(N-1,N) ] spin n spin p Molecules of Generalized Cooper Cooper pairs fermionic atoms pairs of fermionic atoms kF BEC of weakly BCS - BEC BCS superconductivity bound molecules crossover Cooper pairs: correlated momentum-space pairing BCS-BEC crossover for example: Eagles, Leggett, Nozieres and Schmitt-Rink, Randeria, Strinati, Zwerger, Holland, Timmermans, Griffin, Levin … Cooling a gas of fermionic 40K atoms 1. Laser cooling and trapping of 40K 300 K to 1 mK a109 atoms 2.
    [Show full text]
  • The Phases of Warm-Dense Hydrogen and Helium As Seen by Quantum Monte Carlo M
    The Phases of Warm-Dense Hydrogen and Helium as seen by Quantum Monte Carlo M. Morales, DMC: University of Illinois C. Pier leon i: L’Aqu ila, ITALY Eric Schwegler: Livermore • The coupled electron-ion Monte Carlo method • Hydrogen and Helium at High Pressure Supported by DOE DE-FG52-06NA26170 Computer time from NCSA and ORNL (INCITE grant) David Ceperley, UIUC March 4, 2010 KITP Materials Design • Giant Planets – Primary components are H and He –P(ρ,T,xi) closes set of hydrostatic equations – Interior models depend very sensitively on EOS and phase diagram • Saturn’s Luminosity – Homogeneous evolutionary models do not work for Saturn – Additional energy source in planet’s interior is needed – Does it come from Helium Taken from: Fortney J. J., Science 305, 1414 (2004). segregation (rain)? 2 EOS does matter how big is Jit’Jupiter’s core? Planet modeling needs P(ρ,TxT,x) accurate to 1%! Also entropy, compressibility,…. 3 QMC methods for Dense Hydrogen Path Integral MC for T > EF/10 Coupled-electron Ion MC Path Integral MC with an effective potential Diffusion MC T=0 4 MD and MC Simulations –Hard sphere MD/MC ~1953 (Metropolis, Alder) –Empirical potentials (e.g. Lennard-Jones) ~1960 (Verlet, Rahman) –Local density functional theory ~1985 (Car-Parrinello) –Quantum Monte Carlo (CEIMC) ~2000 • Initial simulations used semi-empirical potentials. • Much progress with “ab initio” molecular dynamics simulations where the effects of electrons are solved for each step. • However, the potential surface as determined by density functi ona l theory is not always accurate enough • QMC+MD =CEIMC/MD is a candidate for petascale computing 5 QuantumMonte Carlo • Premise: we need to use simulation techniques to “solve” many-body quantum problems just as you need them classically.
    [Show full text]
  • Lo^ Wc-Rangf Forces Computer Simulation
    ' ^, .*£*' % LO^WC-RANG F FORCES COMPUTER SIMULATION CONDENSED MEDIA i.i.r'.bl-'.v.j (..%-•[-! i..T i' • i '.i rk . C .\jiti irtiM \'. i.:. r ••. c- i i. i ° t-' 0 Hi r* PROCEEDINGS OF THE WORKSHOP THE PROBLEM OF LONG-RANGE FORCES IN THE COMPUTER SIMULATION OF CONDENSED MEDIA Sponsored by the National Resource for Computation in Chemistry Lawrence Berkeley Laboratory Berkeley, California 94720 Held at Vallambrosa Center Menlo Park, California January 8-11, 1980 NRCC Proceedings No. 9 Edited by: David Ceperely -m- CONTENTS Workshop Participants vii Foreword xi Introduction xii SESSION I. CONTROLLED STUDIES OF LONG-RANGE FORCE PROBLEM IN SIMULATION OF IONIC SYSTEMS Review Talk--The Problem of Coulombic Forces in Computer Simulation J. P. Valleau 3 Perturbation Theory for Hard Spheres B. Larsen and S. A. Rogde 9 Periodic Boundary Conditions in Simulation of Ionic Solids E. R. Smith 10 An Alternative to the Ewald Summation? D. J. Adams 11 Periodic, Truncated-Octahedral Boundary Conditions D. J. Adams 13 Summary of Session I B. Larsen 14 SESSION II. CONTROLLED STUDIES OF LONG-RANGE FORCE PROBLEM IN SIMULATION OF DIPOLAR SYSTEMS Review Talk—Dipolar Fluids G. N. Patey 19 Calculation of (k, ) by Computer Simulations of Permanent Dipolar Systems E. L. Pollock 23 Periodic Boundary Conditions for Dipolar Systems E. R. Smith 24 Computer Simulations of Hydrogen-bonded Liquids W. L. Jorgensen 25 -Tv- Dielectric Theory for Polar Molecules with Fluctuating Polarizability G. Stell 27 Summary of Session II J. J. Weis 28 SESSION III. EFFECT OF LONG-RANGE FORCES ON THE SIMULATION OF SOLVATION AND ON BIOPOLYMER HYDRATION: COULOMB AND HYDRODYNAMIC FORCES Review Talk P.
    [Show full text]
  • Optical Lattices and Artificial Gauge Potentials
    Optical Lattices and Artificial Gauge Potentials Juliette Simonet Institute of Laser Physics, Hamburg University Optical Lattices and Artificial Gauge Potentials Part 1: Build up the Hamiltonian Optical Lattices Non-interacting properties (band structure, wave functions) Hubbard models Cold atoms simulator Part 2: Read out the quantum state Probing quantum gases in optical lattice Mapping phase diagrams of Hubbard models Part 3: Beyond Hubbard models in optical lattices Topological properties and transport Magnetic phenomena for neutral atoms 2 Optical Lattices and Artificial Gauge Potentials Part 2: Read Out the Quantum State Part 2 2.1 Probing quantum gases in optical lattices 2.2 Bose-Hubbard Model 2.3 Fermi-Hubbard Model 3 2.1 Probing quantum gases in optical lattices • Momentum space » Time-of-flight measurement (TOF) » Band mapping • Real space: Quantum Gas Microscopes » Single site / single atom detection » Occupation number at each lattice site • Excitation spectrum » Bragg spectroscopy » Amplitude modulation 4 Momentum Space / Time-of-flight measurement • Time-of-flight measurement (TOF) » Sudden extinction of lattice and trap potentials (Projection onto free momentum states) » Free expansion of the atomic cloud under gravity (interactions neglected due to low density) » Absorption imaging with resonant laser light Thermal atoms BEC 5 Momentum Space / Time-of-flight measurement • Time-of-flight measurement (TOF) » Sudden extinction of lattice and trap potentials (Projection onto free momentum states) » Free expansion of the atomic
    [Show full text]