Fermi Surface Reconstruction Without Symmetry Breaking
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Arxiv:2007.10198V2 [Math.NA] 5 Nov 2020
ON THE VALIDITY OF COMPLEX LANGEVIN METHOD FOR PATH INTEGRAL COMPUTATIONS∗ ZHENNING CAIy , XIAOYU DONGz , AND YANG KUANGx Abstract. The complex Langevin (CL) method is a classical numerical strategy to alleviate the numerical sign problem in the computation of lattice field theories. Mathematically, it is a simple numerical tool to compute a wide class of high- dimensional and oscillatory integrals. However, it is often observed that the CL method converges but the limiting result is incorrect. The literature has several unclear or even conflicting statements, making the method look mysterious. By an in-depth analysis of a model problem, we reveal the mechanism of how the CL result turns biased as the parameter changes, and it is demonstrated that such a transition is difficult to capture. Our analysis also shows that the method works for any observables only if the probability density function generated by the CL process is localized. To generalize such observations to lattice field theories, we formulate the CL method on general groups using rigorous mathematical languages for the first time, and we demonstrate that such localized probability density function does not exist in the simulation of lattice field theories for general compact groups, which explains the unstable behavior of the CL method. Fortunately, we also find that the gauge cooling technique creates additional velocity that helps confine the samples, so that we can still see localized probability density functions in certain cases, as significantly broadens the application of the CL method. The limitations of gauge cooling are also discussed. In particular, we prove that gauge cooling has no effect for Abelian groups, and we provide an example showing that biased results still exist when gauge cooling is insufficient to confine the probability density function. -
Quantum Mechanics Quantum Chromodynamics (QCD)
Quantum Mechanics_quantum chromodynamics (QCD) In theoretical physics, quantum chromodynamics (QCD) is a theory ofstrong interactions, a fundamental forcedescribing the interactions between quarksand gluons which make up hadrons such as the proton, neutron and pion. QCD is a type of Quantum field theory called a non- abelian gauge theory with symmetry group SU(3). The QCD analog of electric charge is a property called 'color'. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of Particle physics. A huge body of experimental evidence for QCD has been gathered over the years. QCD enjoys two peculiar properties: Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do split the quark the energy is enough to create another quark thus creating another quark pair; they are forever bound into hadrons such as theproton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD. Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma. This prediction of QCD was first discovered in the early 1970s by David Politzer and by Frank Wilczek and David Gross. For this work they were awarded the 2004 Nobel Prize in Physics. There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant. -
Graphene Reveals Its Strange Side
VIEWPOINT Graphene Reveals Its Strange Side Experiments on magic-angle graphene reveal a ``strange metal'' phase and transport behavior consistent with so-called Planckian dissipation. by Subir Sachdev∗ with a low-temperature transport behavior called Planckian dissipation [2, 3]. The same association is found by Jarillo- agic-angle graphene captured the attention of Herrero and colleagues in magic-angle graphene, providing condensed-matter physicists in 2018 when it further evidence that strange metals are united by a funda- was discovered that this material—made of two mentally new form of transport that theorists are busy trying sheets of graphene with slightly misaligned lat- to characterize. Mtice orientations (Fig. 1)—is a superconductor. Moreover, The transport of electrical and heat currents in metals was observations showed that the phase diagram of magic- once a well-understood corner of condensed-matter physics. angle graphene is similar to that of copper oxide high- This understanding was based on the Drude formula, which temperature superconductors, with an insulating region relates the electrical conductivity to the density of mobile next to a dome-shaped superconducting region (see Trend: electrons, the mass of an electron, and the time between Bilayer Graphene’s Wicked, Twisted Road). Now, Pablo scattering events, t. The original theory, developed by Paul Jarillo-Herrero from the Massachusetts Institute of Technol- Drude in 1900, treated the electrons as classical particles and ogy, Cambridge, and his colleagues report that magic-angle largely ignored electron-electron interactions. Remarkably, graphene has another remarkable feature of the cuprate Drude’s formula survived a quantum-mechanics update in phase diagram: a “strange metal” phase in which the re- the 1930s, in which the electron mass was replaced by sistivity scales linearly with temperature down to very low the effective mass of an electronic “quasiparticle,” and the temperatures [1]. -
Institute Lecture
Institute Lecture Quantum Mechanics Without Particles Professor Subir Sachdev Department of Physics, Harvard University . Tuesday, 21st January, 2014, Time: 6.00 PM, Venue: L-17, Lecture Hall Complex Abstract Quantum mechanics provides a thorough understanding of the physical properties of most common metals, insulators, and superconductors. Even 23 though we cannot solve the Schrödinger equation for 10 particles, we are able to make progress because the electrons move essentially independent of each other. However, in many modern materials, and particularly in the high temperature superconductors, there are important regimes where the independent-electron paradigm breaks down, and we have to deal with wave functions in which all the electrons are entangled with each other in a non- local manner. Understanding such quantum states, in which no particle-like excitations can be identified, is a major theoretical challenge. In this talk, we will describe recent progress in this field using quantum field theory, string theory, and computer simulations. These advances shed light on many of the puzzling features of phase diagrams of the high temperature superconductors. About the speaker Prof. Subir Sachdev is a distinguished condensed matter physicist. He is very well known for his research on quantum phase transitions, and its application to a variety of quantum materials, such as the high temperature superconductors. His book "Quantum Phase Transitions" (Cambridge University Press) has formed the basis of much subsequent research. More recently, he pioneered the application of string theory to the study of quantum phase transitions in condensed matter physics, such as the superfluid- insulator transition of bosons moving in a lattice. -
Adrian Del Maestro's CV.PDF
Adrian Del Maestro Department of Physics University of Vermont 82 University Place Burlington, VT 05405 USA Phone: 802-656-0068 Fax: 802-656-0817 Email: [email protected] URL: http://www.delmaestro.org/adrian/ Education Ph.D. in Physics, 2008. Thesis: The superconductor-metal quantum phase transition in ultra-narrow wires. Supervisor: Subir Sachdev. Harvard University, Cambridge, MA, USA M.S. in Physics, 2005 Yale University, New Haven, CT, USA M.Sc. in Physics, 2003. Thesis: Quantum spin fluctuations in the Heisenberg-like pyrochlore antiferromagnet gadolinium titanate. Supervisor: Michel Gingras. University of Waterloo, Waterloo, ON, Canada B.Sc. in Physics joint with Mathematics, 2002. Graduated summa cum laude. University of Waterloo, Waterloo, ON, Canada Professional Experience Assistant Professor of Physics University of Vermont (Burlington, VT, USA) 2011–Present Distinguished Postdoctoral Fellow Institute for Quantum Matter, Johns Hopkins University (Baltimore, MD, USA) 2010–2011 Postdoctoral Research Scientist University of British Columbia (Vancouver, BC, Canada) 2008 Research Scientist Harvard University (Cambridge, MA, USA) 2008– 2008 System Administrator Harvard University (Cambridge, MA, USA) 2006– 2008 Lab Technician University of Western Ontario, Brain Research Laboratories (London, ON, Canada) 1999 Publications (30 total, h-index: 15, citations: 597) 1. C. M. Herdman, P.-N. Roy, R.G. Melko and A. Del Maestro, Entanglement area law in superfluid 4He, Nature Phys. 4075, 1 (2017). 2. Adrian Del Maestro and Massimo Boninsegni, Absence of superfluidity in a quasi-one-dimensional parahydrogen fluid adsorbed inside carbon nanotubes, Phys. Rev. B 95, 054517 (2017). 3. C. M. Herdman, P.-N. Roy, R. G. Melko and A. Del Maestro, Spatial entanglement entropy in the ground state of the Lieb-Liniger model, Phys. -
Quantum Conductors in a Plane
Proc. Natl. Acad. Sci. USA Vol. 96, pp. 9983–9984, August 1999 From the Academy This paper is a summary of a session presented at the tenth annual symposium on Frontiers of Science, held November 19–21, 1998, at the Arnold and Mabel Beckman Center of the National Academies of Sciences and Engineering in Irvine, CA. Quantum conductors in a plane PHILIP PHILLIPS*†,SUBIR SACHDEV‡,SERGEY KRAVCHENKO§, AND ALI YAZDANI* *Loomis Laboratory of Physics, University of Illinois at Urbana-Champaign, 1100 West Green Street, Urbana, IL 61801-3080; ‡Department of Physics, P.O. Box 208120, Yale University, New Haven, CT 06520; and §Department of Physics, Northeastern University, Boston, MA 02115 When electrons are confined to move in a plane, strange things not a sufficient condition for superconductivity. If one envi- happen. For example, under normal circumstances, they are sions dividing a material into partitions, insulating behavior not expected to conduct electricity at low temperatures. The obtains if each partition at each snapshot in time has the same absence of electrical conduction in two dimensions (2D) at number of Cooper pairs. That is, the state is static. However, zero temperature has been one of the most cherished para- if the number of pairs fluctuates between partitions, transport digms in solid-state physics (1). In fact, the 1977 physics Nobel of Cooper pairs is possible and superconductivity obtains. Prize was awarded, in part, for the formulation of the basic The fundamental physical principle that drives all quantum principle on which this result is based. However, recent phase transitions is quantum uncertainty or quantum entan- experiments (2) on a dilute electron gas confined to move at glement. -
Condensed Matter and Ads/CFT 3 Tems, Almost All of Which Are Not Exactly Solvable
Condensed matter and AdS/CFT Subir Sachdev Lectures at the 5th Aegean summer school, “From gravity to thermal gauge the- ories: the AdS/CFT correspondence”, Adamas, Milos Island, Greece, September 21-26, 2009, and the De Sitter Lecture Series in Theoretical Physics 2009, University of Groningen, November 16-20, 2009. Abstract I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspon- dence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I de- scribe how relativistic structures arise in models of physical interest, present re- sults for their quantum critical crossover functions and magneto-thermoelectric hy- drodynamics. The second class concerns symmetry breaking transitions of two- dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scal- ing structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS du- als. arXiv:1002.2947v1 [hep-th] 16 Feb 2010 Subir Sachdev Department of Physics, Harvard University, Cambridge MA 02138, e-mail: [email protected] 1 2 Subir Sachdev 1 Introduction The past couple of decades have seen vigorous theoretical activity on the quantum phases and phase transitions of correlated electron systems in two spatial dimen- sions. Much of this work has been motivated by the cuprate superconductors, but the list of interesting materials continues to increase unabated [1]. -
New Horizons in Quantum Matter Physics Next: from Quantum Fields to Condensed Matter
New Horizons in Quantum Matter Physics Next: From Quantum Fields to Condensed Matter Hyatt Place Long Island Hotel, NY Aug 24-26, 2017 Subir Sachdev Talk online: sachdev.physics.harvard.edu HARVARD Quantum condensed matter physics before the 1980s: The ground state of metals and insulators is adiabatically connected to the free electron state Excitations are electron-like quasiparticles Pairing of electrons into Cooper pairs, and their condensation leads to superconductivity Breaking of symmetry describes superconductivity, ferromagnetism, antiferromagnetism, and other ordered states Hints of physics beyond quasiparticles: the Wilson-Fisher theory of the Ising transition at finite temperature, the theory of dynamic critical phenomena, Nozieres-Blandin multi- channel Kondo critical point Quantum condensed matter physics before the 1980s: The ground state of metals and insulators is adiabatically connected to the free electron state Excitations are electron-like quasiparticles Pairing of electrons into Cooper pairs, and their condensation leads to superconductivity Breaking of symmetry describes superconductivity, ferromagnetism, antiferromagnetism, and other ordered states Hints of physics beyond quasiparticles: the Wilson-Fisher theory of the Ising transition at finite temperature, the theory of dynamic critical phenomena, Nozieres-Blandin multi- channel Kondo critical point VOI vM+ $5s +vMQ&R PHYSIC:AI. REVIEW LETTERS 11 AvGvsY 1980 ew et od for High-Accuracy Determination of th e Fine--Structure Constant Based on Quantized Hall Resistance K. v. Klitzing Hsysikalisches Institut der Universitat Wurzburg, D-8700 ~iirgburg,urgburg, FederalI'ederal RepublicRe b of Germany, and IIochfeld-Ma gn etlabor des Max-Planckx- anc --Insnstitutstitut pier PestkorPerforsckung, P 38048-Grenoble, Prance G. Dorda Forschungslaboratorien der Siemens AG, D-80000 Mununcken,ThePedera/ integerRePublic of quantumGermany Hall effect and VOI vM+ $5s +vMQ&R PHYSIC:AI. -
Topological Order, Emergent Gauge Fields, and Fermi Surface
arXiv:1801.01125 Topological order, emergent gauge fields, and Fermi surface reconstruction Subir Sachdev Department of Physics, Harvard University, Cambridge MA 02138, USA Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5 Department of Physics, Stanford University, Stanford CA 94305, USA E-mail: [email protected] December 2017 Abstract. This review describes how topological order associated with the presence of emergent gauge fields can reconstruct Fermi surfaces of metals, even in the absence of translational symmetry breaking. We begin with an introduction to topological order using Wegner's quantum Z2 gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying Z2 magnetic flux. The interplay between topological order and the breaking of global symmetry is described by the non-zero temperature statistical mechanics of classical XY models in dimension D = 3; such models also describe the zero temperature quantum phases of bosons with short-range interactions on the square lattice at integer filling. The topological state is again characterized by the expulsion of certain defects, in a state with fluctuating symmetry-breaking order, along with the presence of emergent gauge fields. The phase diagrams of the Z2 gauge theory and the XY models are obtained by embedding them in U(1) gauge theories, and by studying their Higgs and confining phases. These ideas are then applied to the single-band Hubbard model on the square lattice. A SU(2) gauge theory describes the fluctuations of spin-density-wave order, and its phase diagram is presented by analogy to the XY models. -
Field Theory Research Team
Chapter 5 Field Theory Research Team 5.1 Members Yoshinobu Kuramashi (Team Leader) Yoshifumi Nakamura (Research Scientist) Hiroya Suno (Research Scientist, Joint Position with the Nishina Center for Accelerator-based Research) Eigo Shintani (Research Scientist) Yuya Shimizu (Postdoctoral Researcher) Yusuke Yoshimura (Postdoctoral Researcher) Ken-Ichi Ishikawa (Visiting Scientist, Hiroshima University) Takeshi Yamazaki (Visiting Scientist, University of Tsukuba) Shinji Takeda (Visiting Scientist, Kanazawa University) 5.2 Research Activities Our research field is physics of elementary particles and nuclei, which tries to answer questions in history of mankind: What is the smallest component of matter and what is the most fundamental interactions? This research subject is related to the early universe and the nucleosynthesis through Big Bang cosmology. Another important aspect is quantum properties, which play an essential role in the world of elementary particles and nuclei as well as in the material physics at the atomic or molecular level. We investigate nonperturbative properties of elementary particles and nuclei through numerical simulations with the use of lattice QCD (Quantum ChromoDynamics). The research is performed in collaboration with applied mathematicians, who are experts in developing and improving algorithms, and computer scientists responsible for research and development of software and hardware systems. Lattice QCD is one of the most advanced case in quantum sciences: Interactions between quarks, which are elementary particles known to date, are described by QCD formulated with the quantum field theory. We currently focus on two research subjects: (1) QCD at finite temperature and finite density. We try to understand the early universe and the inside of neutron star by investigating the phase structure and the equation of state. -
Arxiv:1808.05659V4 [Hep-Th] 29 Jun 2021
NORDITA 2018-074 Slow relaxation and diffusion in holographic quantum critical phases Richard A. Davison∗ Department of Physics, Harvard University, Cambridge MA 02138 USA and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom Simon A. Gentley Institute for Theoretical Physics, Utrecht University, 3508TD Utrecht, The Netherlands and Instituut-Lorentz for Theoretical Physics, Leiden University, 2333CA Leiden, The Netherlands and Blaise Gout´erauxz Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden (Dated: June 30, 2021) arXiv:1808.05659v4 [hep-th] 29 Jun 2021 1 Abstract The dissipative dynamics of strongly interacting systems are often characterised by the timescale set by the inverse temperature τP ∼ ~=(kBT ). We show that near a class of strongly interacting quantum critical points that arise in the infra-red limit of translationally invariant holographic theories, there is a collective excitation (a quasinormal mode of the dual black hole spacetime) −1 whose lifetime τeq is parametrically longer than τP : τeq T . The lifetime is enhanced due to its dependence on a dangerously irrelevant coupling that breaks the particle-hole symmetry and the invariance under Lorentz boosts of the quantum critical point. The thermal diffusivity (in units of the butterfly velocity) is anomalously large near the quantum critical point and is governed by τeq rather than τP . We conjecture that there exists a long-lived, propagating collective mode with 2 velocity vs, and in this case the relation D = vs τeq holds exactly in the limit T τeq 1. While scale invariance is broken, a generalised scaling theory still holds provided that the dependence of observables on the dangerously irrelevant coupling is incorporated. -
New Insights Into the Sign Problem of Qcd and Heavy Tetraquarks
ABSTRACT Title of dissertation: NEW INSIGHTS INTO THE SIGN PROBLEM OF QCD AND HEAVY TETRAQUARKS Yiming Cai Doctor of Philosophy, 2020 Dissertation directed by: Thomas Cohen Department of Physics Quantum Chromodynamics (QCD) describes strong interactions among the fundamental particles known as quarks and gluons. In principle, QCD can be used to explain complicated phenomena in the strong sector. However, at the energy scale of hadronic physics, the strong coupling constant is so large that the traditional per- turbative method is not applicable. There are two powerful alternative approaches utilized in the non-pertubative regime: (1) lattice QCD, which discretizes space-time and utilizes Monte Carlo computer simulations, and (2) finding new systematic ex- pansion regimes to obtain physical insights in certain limits. In this dissertation, three problems are studied in the context of these two approaches. In Chapter 2, a notorious numeric problem in lattice QCD known as the sign problem is explored. A subtle phenomenon caused by the interplay between the sign problem and the infinite volume limit is discussed and explained using the saddle point approximation. This work provides insight into the sign problem and the physics of the QCD θ-vacuum. Chapter 3 and Chapter 4 focus on tetraquarks, which are unconventional hadrons containing four valence quarks. Despite numerous tetraquark candidates seen in experiments, there is no unified and well-accepted theoretical descriptions of the tetraquark state yet. This dissertation examines the existence of tetraquarks in the heavy quark mass limit. A powerful systematic expansion regime can be built when the heavy quark mass is extremely large.