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Anyon Theory in Gapped Many-Body Systems from Entanglement
Anyon theory in gapped many-body systems from entanglement Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Bowen Shi, B.S. Graduate Program in Department of Physics The Ohio State University 2020 Dissertation Committee: Professor Yuan-Ming Lu, Advisor Professor Daniel Gauthier Professor Stuart Raby Professor Mohit Randeria Professor David Penneys, Graduate Faculty Representative c Copyright by Bowen Shi 2020 Abstract In this thesis, we present a theoretical framework that can derive a general anyon theory for 2D gapped phases from an assumption on the entanglement entropy. We formulate 2D quantum states by assuming two entropic conditions on local regions, (a version of entanglement area law that we advocate). We introduce the information convex set, a set of locally indistinguishable density matrices naturally defined in our framework. We derive an isomorphism theorem and structure theorems of the information convex sets by studying the internal self-consistency. This line of derivation makes extensive usage of information-theoretic tools, e.g., strong subadditivity and the properties of quantum many-body states with conditional independence. The following properties of the anyon theory are rigorously derived from this framework. We define the superselection sectors (i.e., anyon types) and their fusion rules according to the structure of information convex sets. Antiparticles are shown to be well-defined and unique. The fusion rules are shown to satisfy a set of consistency conditions. The quantum dimension of each anyon type is defined, and we derive the well-known formula of topological entanglement entropy. -
CERN Courier–Digital Edition
CERNMarch/April 2021 cerncourier.com COURIERReporting on international high-energy physics WELCOME CERN Courier – digital edition Welcome to the digital edition of the March/April 2021 issue of CERN Courier. Hadron colliders have contributed to a golden era of discovery in high-energy physics, hosting experiments that have enabled physicists to unearth the cornerstones of the Standard Model. This success story began 50 years ago with CERN’s Intersecting Storage Rings (featured on the cover of this issue) and culminated in the Large Hadron Collider (p38) – which has spawned thousands of papers in its first 10 years of operations alone (p47). It also bodes well for a potential future circular collider at CERN operating at a centre-of-mass energy of at least 100 TeV, a feasibility study for which is now in full swing. Even hadron colliders have their limits, however. To explore possible new physics at the highest energy scales, physicists are mounting a series of experiments to search for very weakly interacting “slim” particles that arise from extensions in the Standard Model (p25). Also celebrating a golden anniversary this year is the Institute for Nuclear Research in Moscow (p33), while, elsewhere in this issue: quantum sensors HADRON COLLIDERS target gravitational waves (p10); X-rays go behind the scenes of supernova 50 years of discovery 1987A (p12); a high-performance computing collaboration forms to handle the big-physics data onslaught (p22); Steven Weinberg talks about his latest work (p51); and much more. To sign up to the new-issue alert, please visit: http://comms.iop.org/k/iop/cerncourier To subscribe to the magazine, please visit: https://cerncourier.com/p/about-cern-courier EDITOR: MATTHEW CHALMERS, CERN DIGITAL EDITION CREATED BY IOP PUBLISHING ATLAS spots rare Higgs decay Weinberg on effective field theory Hunting for WISPs CCMarApr21_Cover_v1.indd 1 12/02/2021 09:24 CERNCOURIER www. -
The ATLAS Experiment
The ATLAS Experiment Mapping the Secrets of the Universe Michael Barnett Physics Division July 2007 With help from: Joao Pequenao Paul Schaffner M. Barnett – July 2007 1 Large Hadron Collider CERN lab in Geneva Switzerland Protons will circulate in opposite directions and collide inside experimental areas 100 meters underground 17 miles around M. Barnett – July 2007 2 The ATLAS Experiment See animation M. Barnett – July 2007 3 Large Hadron Collider Numbers The fastest racetrack on the planet Trillions of protons will race around the 17-mile ring 11,000 times a second, traveling at 99.9999991% the speed of light. Seven times the energy of any previous accelerator. The emptiest space in the solar system Accelerating protons to almost the speed of light requires a vacuum as empty as interplanetary space. There is 10 times more atmosphere on the moon than there will be in the LHC. M. Barnett – July 2007 4 Large Hadron Collider Numbers The hottest spot in our galaxy Colliding protons will generate temperatures 100,000 times hotter than the sun (but in a minuscule space). Equivalent to a billionth of a second after the Big Bang M. Barnett – July 2007 5 LHC Exhibition at London Science Museum M. Barnett – July 2007 6 Large Hadron Collider Numbers The biggest most sophisticated detectors ever built Recording the debris from 600 million proton collisions per second requires building gargantuan devices that measure particles with 0.0004 inch precision. The most extensive computer system in the world Analyzing the data requires tens of thousands of computers around the world using the Grid. -
Aaron Taylor Physics and Astronomy This
Aaron Taylor Candidate Physics and Astronomy Department This dissertation is approved, and it is acceptable in quality and form for publication: Approved by the Dissertation Committee: Dr. Sally Seidel , Chairperson Dr. Pavel Reznicek Dr. Huaiyu Duan Dr. Douglas Fields Dr. Bruce Schumm CERN-THESIS-2017-006 04/11/2016 SEARCH FOR NEW PHYSICS PROCESSES WITH HEAVY QUARK SIGNATURES IN THE ATLAS EXPERIMENT by AARON TAYLOR B.A., Mathematics, University of California, Santa Cruz, 2011 M.S., Physics, University of New Mexico, 2014 DISSERTATION Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Physics The University of New Mexico Albuquerque, New Mexico May, 2017 ©2017, Aaron Taylor iii Acknowledgements I would like to thank Professor Sally Seidel, for her constant support and guidance in my research. I would also like to thank her for her patience in helping me to develop my technical writing and presentation skills; without her assistance, I would never have gained the skill I have in that field. I would like to thank Konstantin Toms, for his constant assistance with the ATLAS code, and for generally giving advice on how to handle data analysis. The Bs → 4μ analysis likely wouldn’t have gotten anywhere without him. I would like to deeply thank Pavel Reznicek, without whom I would never have gotten as great an understanding of ATLAS code as I currently have. It is no exaggeration to say that I would not have been half as successful as I have been without his constant patience and understanding. Thank you. Many thanks to Martin Hoeferkamp, who taught me much about instrumentation and physical measurements. -
Email Issues
EMAIL ISSUES - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - TABLE OF CONTENTS NEW POLICY WITH RESPECT TO EMAIL ADDRESSES A NECESSARY EMAIL SETTING WHY OUR EMAILS POSSIBLY ARRIVED LATE OR NOT AT ALL STOP USING YAHOO, NETZERO, AND JUNO EMAIL PROVIDERS - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - NEW POLICY WITH RESPECT TO EMAIL ADDRESSES: There are two important issues here. FIRST, members must not supply CFIC with their company email addresses. That is, companies that they work for. (If you own the company, that's different.) All email on a company's server can be read by any supervisor. All it takes is one pro vaccine activist to get hold of our mobilization alerts to throw a monkey wrench in all of our efforts. Thus, do not supply me with a company email address. We can help you get an alternative to that if necesary. SECONDLY, CFIC needs members' email addresses to supply important information to mobilize parents to do things that advances our goal to enact our legislative reforms of the exemptions from vaccination. That has always been CFIC's sole agenda. CFIC has been able to keep the membership fee to zero because we don't communicate via snail mail. But people change their addresses frequently and forget to update CFIC. When this happens over the years, that member is essentually blind and deaf to us, and is no longer of any value to the coalition---your fellow parents. Therefore, it warrants me to require that members supply CFIC with their most permanent email account. That means the email address of the company in which you are paying a monthly fee for internet access, be it broadband or dialup service. -
Sensitivity Study and First Prototype Tests for the CHIPS Neutrino
Sensitivity study and first prototype tests for the CHIPS neutrino detector R&D program Maciej Marek Pfützner University College London Submitted to University College London in fulfilment of the requirements for the award of the degree of Doctor of Philosophy July 20, 2018 1 2 Declaration I, Maciej Marek Pfützner confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. Maciej Pfützner 3 4 Abstract CHIPS (CHerenkov detectors In mine PitS) is an R&D project aiming to develop novel cost-effective detectors for long baseline neutrino oscillation experiments. Water Cherenkov detector modules will be submerged in an existing lake in the path of an accelerator neutrino beam, eliminating the need for expensive excavation. In a staged approach, the first detectors will be deployed in a flooded mine pit in northern Minnesota, 7 mrad off-axis from the existing NuMI beam. A small proof-of-principle model (CHIPS-M) has already been tested and the first stage of a fully functional 10 kt module (CHIPS-10) is planned for 2018. The main physics aim is to measure the CP-violating neutrino mixing phase (δCP). A sensitivity study was performed with the GLoBES package, using results from a dedicated detector simulation and a preliminary reconstruction algorithm. The predicted physics reach of CHIPS-10 and potential bigger modules is presented and compared with currently running experiments and future projects. One of the instruments submerged on board CHIPS-M in autumn 2015 was a prototype detection unit, constructed at Nikhef. -
A Mislivec, Minerva Coherent
Charged Current Coherent Pion Production in MINERνA Aaron Mislivec University of Rochester w/ Aaron Higuera Outline • Motivation • MINERνA Detector and Kinematics Reconstruction • Event Selection • Background Tuning • Contribution from Diffractive Scattering off Hydrogen • Systematics • Cross Sections Aaron Mislivec, University of Rochester NuInt14 2 K. HIRAIDE et al. PHYSICAL REVIEW D 78, 112004 (2008) 100 TABLE III. Event selection summary for the MRD-stopped DATA charged current coherent pion sample. CC coherent π Event selection Data MC Coherent % CC resonant π Signal BG Efficiency Other Generated in SciBar fid.vol. 1939 156 766 100% CC QE 50 SciBar-MRD matched 30 337 978 29 359 50.4% MRD-stopped 21 762 715 20 437 36.9% two-track 5939 358 6073 18.5% Entries / 5 degrees Particle ID (" %) 2255 292 2336 15.1% Vertex activityþ cut 887 264 961 13.6% CCQE rejection 682 241 709 12.4% 0 0 20 40 60 80 100 120 140 160 180 Pion track direction cut 425 233 451 12.0% Reconstructed Q2 cut 247 201 228 10.4% ∆θp (degrees) FIG. 11 (color online). Á for the " % events in the MRD p þ stopped sample after fitting. which the track angle of the pion candidate with respect to the beam direction is less than 90 degrees are selected. Figure 13 shows the reconstructed Q2 distribution for the " % events after the pion track direction cut. Althoughþ a charged current quasielastic interaction is as- DATA 80 sumed, the Q2 of charged current coherent pion events is CC coherent π reconstructed with a resolution of 0:016 GeV=c 2 and a CC resonant π 2 ð Þ 60 shift of 0:024 GeV=c according to the MC simulation. -
Particle Physics
If you would like to register to receive Fascination automatically ISSUE 11 please visit www.stfc.ac.uk/fascination News from the Cover image: A proton collision at the ATLAS experiment which produced a microscopic-black-hole. Credit: CERN Science and Technology particle Facilities Council Exploring & Understanding Science physics special CONTENTS Benefits of particle physics LHC leads the way on new technology Higgs - The story so far Higgs Boson dominated the news media for two days LHC on tour in the UK Using the very large to look for the extremely small How did the Universe begin? What are we made of? Why are all world class. It represents amazing value for the amount does matter behave the way it does? These are questions of added benefit we get from what is at heart a fundamental that particle physics can answer. Particle physics is an ideal science project. With the recent breakthrough discovery of a showcase for STFC’s work – a subject where the research, the Higgs-like particle, this edition is focussing on particle physics resultant innovation and the inspirational value of the science and why it matters to the UK. The benefits of particle physics to you and everyone you know nature of matter, the so called known unknowns, and in the process uncover new questions we have yet to answer. It’s a compellingly difficult search that pushes our understanding of matter beyond the limits of what was previously possible. But the search is expensive, times are tough and costs need to be justified, so the secondary benefits from the research are often just as important. -
Introduction to Abelian and Non-Abelian Anyons
Introduction to abelian and non-abelian anyons Sumathi Rao Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India. In this set of lectures, we will start with a brief pedagogical introduction to abelian anyons and their properties. This will essentially cover the background material with an introduction to basic concepts in anyon physics, fractional statistics, braid groups and abelian anyons. The next topic that we will study is a specific exactly solvable model, called the toric code model, whose excitations have (mutual) anyon statistics. Then we will go on to discuss non-abelian anyons, where we will use the one dimensional Kitaev model as a prototypical example to produce Majorana modes at the edge. We will then explicitly derive the non-abelian unitary matrices under exchange of these Majorana modes. PACS numbers: I. INTRODUCTION The first question that one needs to answer is why we are interested in anyons1. Well, they are new kinds of excitations which go beyond the usual fermionic or bosonic modes of excitations, so in that sense they are like new toys to play with! But it is not just that they are theoretical constructs - in fact, quasi-particle excitations have been seen in the fractional quantum Hall (FQH) systems, which seem to obey these new kind of statistics2. Also, in the last decade or so, it has been realised that if particles obeying non-abelian statistics could be created, they would play an extremely important role in quantum computation3. So in the current scenario, it is clear that understanding the basic notion of exchange statistics is extremely important. -
Fabiola Gianotti
Fabiola Gianotti Date of Birth 29 October 1960 Place Rome, Italy Nomination 18 August 2020 Field Physics Title Director-General of the European Laboratory for Particle Physics, CERN, Geneva Most important awards, prizes and academies Honorary Professor, University of Edinburgh; Corresponding or foreign associate member of the Italian Academy of Sciences (Lincei), the National Academy of Sciences of the United States, the French Academy of Sciences, the Royal Society London, the Royal Academy of Sciences and Arts of Barcelona, the Royal Irish Academy and the Russian Academy of Sciences. Honorary doctoral degrees from: University of Uppsala (2012); Ecole Polytechnique Federale de Lausanne (2013); McGill University, Montreal (2014); University of Oslo (2014); University of Edinburgh (2015); University of Roma Tor Vergata (2017); University of Chicago (2018); University Federico II, Naples (2018); Université de Paris Sud, Orsay (2018); Université Savoie Mont Blanc, Annecy (2018); Weizmann Institute, Israel (2018); Imperial College, London (2019). National honours: Cavaliere di Gran Croce dell'Ordine al Merito della Repubblica, awarded by the Italian President Giorgio Napolitano (2014). Special Breakthrough Prize in Fundamental Physics (shared, 2013); Enrico Fermi Prize of the Italian Physical Society (shared, 2013); Medal of Honour of the Niels Bohr Institute, Copenhagen (2013); Wilhelm Exner Medal, Vienna (2017); Tate Medal of the American Institute of Physics for International Leadership (2019). Summary of scientific research Fabiola Gianotti is a particle physicist working at high-energy accelerators. In her scientific career, she has made significant contributions to several experiments at CERN, including UA2 at the proton-antiproton collider (SpbarpS), ALEPH at the Large Electron-Positron collider (LEP) and ATLAS at the Large Hadron Collider (LHC). -
Migrationsleitfaden
Migrationsleitfaden Leitfaden für die Migration der Basissoftwarekomponenten auf Server- und Arbeitsplatz-Systemen Version 1.0 – Juli 2003 Schriftenreihe der KBSt ISSN 0179-7263 Band 57 Juli 2003 Schriftenreihe der KBSt Band 57 ISSN 0179 - 7263 Nachdruck, auch auszugsweise, ist genehmigungspflichtig Dieser Band wurde erstellt von der KBSt im Bundesministeri- um des Innern in Zusammenarbeit mit dem Bundesamt für Sicherheit in der Informationstechnik (BSI), dem Bundesver- waltungsamt (BVA) und der C_sar Consulting, solutions and results AG Redaktion: C_sar AG, Berlin Interessenten erhalten die derzeit lieferbaren Veröffentlichungen der KBSt und weiterführende Informationen zu den Dokumenten bei Bundesministerium des Innern Referat IT 2 (KBSt) 11014 Berlin Tel.: +49 (0) 1888 681 - 2312 Fax.: +49 (0) 1888 681 - 523121 Homepage der KBSt: http://www.kbst.bund.de 1Frau Monika Pfeiffer (mailto: [email protected]) Migrationsleitfaden Leitfaden für die Migration der Basissoftwarekomponenten auf Server- und Arbeitsplatz-Systemen Version 1.0 Juli 2003 Herausgegeben vom Bundesministerium des Innern INHALTSVERZEICHNIS 1 Einleitung ........................................................................ 8 1.1 Über das Vorhaben 8 1.2 Über diesen Leitfaden 9 1.3 Hinweise zur Benutzung des Leitfadens 10 1.4 Hinweise an die Entscheider 12 1.4.1 Grundsätzliche Empfehlungen 12 1.4.2 Fortführende und ablösende Migration 13 1.4.3 Migrationswege 14 1.4.4 Vergleichbarkeit von Alternativen 14 1.4.5 Künftige Schwerpunte 15 1.4.6 Wirtschaftlichkeit 16 -
Fermion Condensation and Gapped Domain Walls in Topological Orders
Fermion Condensation and Gapped Domain Walls in Topological Orders Yidun Wan1,2, ∗ and Chenjie Wang2, † 1Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China 2Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada (Dated: September 12, 2018) We propose the concept of fermion condensation in bosonic topological orders in two spatial dimensions. Fermion condensation can be realized as gapped domain walls between bosonic and fermionic topological orders, which are thought of as a real-space phase transitions from bosonic to fermionic topological orders. This generalizes the previous idea of understanding boson conden- sation as gapped domain walls between bosonic topological orders. We show that generic fermion condensation obeys a Hierarchy Principle by which it can be decomposed into a boson condensation followed by a minimal fermion condensation, which involves a single self-fermion that is its own anti-particle and has unit quantum dimension. We then develop the rules of minimal fermion con- densation, which together with the known rules of boson condensation, provides a full set of rules of fermion condensation. Our studies point to an exact mapping between the Hilbert spaces of a bosonic topological order and a fermionic topological order that share a gapped domain wall. PACS numbers: 11.15.-q, 71.10.-w, 05.30.Pr, 71.10.Hf, 02.10.Kn, 02.20.Uw I. INTRODUCTION to condensing self-bosons in a bTO. A particularly inter- esting question is: Is it possible to condense self-fermions, A gapped quantum matter phase with intrinsic topo- which have nontrivial braiding statistics with some other logical order has topologically protected ground state anyons in the system? At a first glance, fermion conden- degeneracy and anyon excitations1,2 on which quantum sation might be counterintuitive; however, in this work, computation may be realized via anyon braiding, which is we propose a physical context in which fermion conden- robust against errors due to local perturbation3,4.