Hamiltonian Models of Lattice Fermions Solvable by the Meron-Cluster Algorithm
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Geometric Lattice Models and Irrational Conformal Field Theories Romain Couvreur
Geometric lattice models and irrational conformal field theories Romain Couvreur To cite this version: Romain Couvreur. Geometric lattice models and irrational conformal field theories. Mathematical Physics [math-ph]. Sorbonne Université, 2019. English. NNT : 2019SORUS062. tel-02569051v2 HAL Id: tel-02569051 https://hal.archives-ouvertes.fr/tel-02569051v2 Submitted on 21 Oct 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE DE DOCTORAT DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Spécialité : Physique École doctorale no564: Physique en Île-de-France réalisée au Laboratoire de Physique Théorique - ENS et à l’Institut de Physique Théorique - CEA sous la direction de Jesper Jacobsen et Hubert Saleur présentée par Romain Couvreur pour obtenir le grade de : DOCTEUR DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Sujet de la thèse : Geometric lattice models and irrational conformal field theories soutenue le 25 juin 2019 devant le jury composé de : M. Paul Fendley Rapporteur M. Ilya Gruzberg Rapporteur M. Jean-Bernard Zuber Examinateur Mme Olalla Castro-Alvaredo Examinatrice M. Benoit Estienne Examinateur M. Jesper Lykke Jacobsen Directeur de thèse M. Hubert Saleur Membre invité (co-directeur) Geometric lattice models and irrational conformal field theories Abstract: In this thesis we study several aspects of two-dimensional lattice models of statistical physics with non-unitary features. -
Dimensional Topological Quantum Field Theory from a Tight-Binding Model of Interacting Spinless Fermions
This is a repository copy of (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/99993/ Version: Accepted Version Article: Cirio, M, Palumbo, G and Pachos, JK (2014) (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions. Physical Review B, 90 (8). 085114. ISSN 2469-9950 https://doi.org/10.1103/PhysRevB.90.085114 Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions Mauro Cirio,1 Giandomenico Palumbo,2 and Jiannis K. Pachos2 1Centre for Engineered Quantum Systems, Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia 2School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, United Kingdom (Dated: July 15, 2014) Currently, there is much interest in discovering analytically tractable (3 + 1)-dimensional models that describe interacting fermions with emerging topological properties. -
Condensed Matter Physics with Light and Atoms: Strongly Correlated Cold Fermions in Optical Lattices
Condensed Matter Physics With Light And Atoms: Strongly Correlated Cold Fermions in Optical Lattices. Antoine Georges Centre de Physique Th´eorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France Lectures given at the Enrico Fermi Summer School on ”Ultracold Fermi Gases” organized by M. Inguscio, W. Ketterle and C. Salomon (Varenna, Italy, June 2006) Summary. — Various topics at the interface between condensed matter physics and the physics of ultra-cold fermionic atoms in optical lattices are discussed. The lec- tures start with basic considerations on energy scales, and on the regimes in which a description by an effective Hubbard model is valid. Qualitative ideas about the Mott transition are then presented, both for bosons and fermions, as well as mean-field theories of this phenomenon. Antiferromagnetism of the fermionic Hubbard model at half-filling is briefly reviewed. The possibility that interaction effects facilitate adiabatic cooling is discussed, and the importance of using entropy as a thermometer is emphasized. Geometrical frustration of the lattice, by suppressing spin long-range order, helps revealing genuine Mott physics and exploring unconventional quantum magnetism. The importance of measurement techniques to probe quasiparticle ex- arXiv:cond-mat/0702122v1 [cond-mat.str-el] 5 Feb 2007 citations in cold fermionic systems is emphasized, and a recent proposal based on stimulated Raman scattering briefly reviewed. The unconventional nature of these excitations in cuprate superconductors is emphasized. c Societ`aItaliana di Fisica 1 2 A. Georges 1. – Introduction: a novel condensed matter physics. The remarkable recent advances in handling ultra-cold atomic gases have given birth to a new field: condensed matter physics with light and atoms. -
Lecture 9 Sine-Gordon Model and Thirring Model Consider the Action
Lecture 9 Sine-Gordon model and Thirring model Consider the action of the sine-Gordon model in the general form Z (@ ')2 S ['] = d2x µ + 2µ cos β' : (1) sG 16π Here the action depends on two parameters: β and µ. Thep parameter β is dimensionless. We may consider it as the square root of the Planck constant: β = ~. Indeed, let u(x) = β'(x). Then the action is 1 Z (@ u)2 S = d2x µ + 2µβ2 cos u : sG β2 16π For β 1 the square of mass of the lightest excitation is m2 = 16πµβ2. If we keep it finite, the only place β enters is the prefactor, which must be ~−1 in the quantum case. We will consider the sine-Gordon theory as a perturbation of a free massless boson. The perturbation operator :cos β': has the scaling dimension 2β2. Hence, the dimension of the parameter µ is 2 − 2β2. Since this is the only dimensional parameter, masses of all particles in the theory must be proportional 2 to µ1=(2−2β ). In the limit β ! 0 we have m / µ1=2 as expected. The behavior of the model depends of the value of β. There are three cases 1. β2 < 1. The dimension of µ is positive, the perturbation is relevant. It means that the interaction decreases with decreasing scale. The short-range correlation functions behave like those in the massless free field theory. It makes the sine-Gordon theory well-defined and superrenormalizable. But the large-distance behavior strikingly differs from the short-distance one. It is described by a system of massive particles, whose mass spectrum essentially depends on the parameter β. -
Lattice Vibration As a Knob for Novel Quantum Criticality: Emergence Of
Lattice vibration as a knob for novel quantum criticality : Emergence of supersymmetry from spin-lattice coupling SangEun Han,1, ∗ Junhyun Lee,2, ∗ and Eun-Gook Moon1, y 1Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea 2Department of Physics, Condensed Matter Theory Center and the Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA (Dated: November 6, 2019) Control of quantum coherence in many-body system is one of the key issues in modern condensed matter. Conventional wisdom is that lattice vibration is an innate source of decoherence, and amounts of research have been conducted to eliminate lattice effects. Challenging this wisdom, here we show that lattice vibration may not be a decoherence source but an impetus of a novel coherent quantum many-body state. We demonstrate the possibility by studying the transverse-field Ising model on a chain with renormalization group and density-matrix renormalization group method, and theoretically discover a stable N = 1 supersymmetric quantum criticality with central charge c = 3=2. Thus, we propose an Ising spin chain with strong spin-lattice coupling as a candidate to observe supersymmetry. Generic precursor conditions of novel quantum criticality are obtained by generalizing the Larkin-Pikin criterion of thermal transitions. Our work provides a new perspective that lattice vibration may be a knob for exotic quantum many-body states. Quantum states on a lattice inevitably couple to lattice vibration, and the coupling is known to be one of the hxˆ main sources of decoherence of quantum states. To be ~si+1 z specific, let us consider a spin system on a lattice whose z s i+1 i Hamiltonian may be schematically written by, ~si -Js 0 0 H = Hspin + Hphonon + gHs−l; i+1 2 u 0 γ 0 where Hspin=phonon is for a pure spin/phonon system, and Mω Hs−l is for the spin-lattice coupling. -
Effective Field Theories for Interacting Boundaries of 3D Topological
www.nature.com/scientificreports OPEN Efective feld theories for interacting boundaries of 3D topological crystalline insulators through bosonisation Patricio Salgado‑Rebolledo1*, Giandomenico Palumbo2 & Jiannis K. Pachos1 Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion interactions the system can be efectively described by a rich variety of topologically massive gauge theories. Among these efective theories, we obtain an extended Chern–Simons theory with higher order derivatives as well as two coupled Chern–Simons theories. Our formalism allows for a general description of interacting fermions emerging, for example, at the gapped boundary of three‑dimensional topological crystalline insulators. Time-reversal-invariant topological insulators are among the most well studied topological phases of matter. In three dimensions, they are characterised by suitable topological numbers in the bulk that guarantee the existence 1,2 of topologically protected massless Dirac fermions on the boundary . Although the topological invariant is a Z2 number, on the slab geometry, it has been shown that robust surface states are given by an odd number of Dirac fermions per boundary3. Te situation changes in the case of three-dimensional topological crystalline insula- tors (TCIs), namely topological insulators characterised by further crystalline symmetries, such as mirror and rotation symmetries4–11. In particular, for three-dimensional TCIs protected by a single mirror symmetry, one can defne the so called mirror Chern number nM on a given two-dimensional plane, which is invariant under 5 the mirror symmetry. -
VARIATIONAL ANALYSIS of the THIRRING MODEL* Sidney
SLAC-PUB-1999 August 1977 (T) FERMION FIELD THEORY ON A LATTICE: VARIATIONAL ANALYSIS OF THE THIRRING MODEL* Sidney D. Drell, Benjamin Svetitsky**, and Marvin Weinstein Stanford Linear Accelerator Center Stanford University, Stanford, California 94305 Abstract We extend variational techniques previously described to study the two-dimensional massless free fermion field and the Thirring model on a spatial lattice, The iterative block spin procedure of con- structing an effective lattice Hamiltonian, starting ,by dissecting the lattice into Z-site blocks, is shown to be successful in producing results known for the continuum Thirring model. Submitted to Phys . Rev. *Work supported by the Energy Research and Development Administration, **National Science Foundation Graduate Fellow in absentia from Princeton University. -2- 1. INTRODUCTION I,n this paper we continue the development and application of techniques for finding the ground state and spectrum of low-lying physical states of field the- ories without recourse to either weak or strong coupling expansioas. Following 1 our earlier papers we study lattice Hamiltonians by means of a constructive variational procedure. The methods, which in our preceding paper (Paper III) were described and applied to free field theory of bosons in oae space dimension and to the one-dimensional Ising model with a transverse applied mag.netic field, are now applied to two fermion theories in lx - It dimensions: massless free 2-5 fermions and the Thirring .model. Our aim in this paper is to demonstrate that these methods are easily applied to fermion theories and that our simple con- structive approach reproduces results known to hold in soluble continuum models. -
Lattice Field Theory Study of Magnetic Catalysis in Graphene
W&M ScholarWorks Arts & Sciences Articles Arts and Sciences 4-24-2017 Lattice field theory study of magnetic catalysis in graphene Carleton DeTar Christopher Winterowd Savvas Zafeiropoulos College of William and Mary, [email protected] Follow this and additional works at: https://scholarworks.wm.edu/aspubs Recommended Citation DeTar, Carleton; Winterowd, Christopher; and Zafeiropoulos, Savvas, Lattice field theory study of magnetic catalysis in graphene (2017). PHYSICAL REVIEW B, 95(16). 10.1103/PhysRevB.95.165442 This Article is brought to you for free and open access by the Arts and Sciences at W&M ScholarWorks. It has been accepted for inclusion in Arts & Sciences Articles by an authorized administrator of W&M ScholarWorks. For more information, please contact [email protected]. This is the accepted manuscript made available via CHORUS. The article has been published as: Lattice field theory study of magnetic catalysis in graphene Carleton DeTar, Christopher Winterowd, and Savvas Zafeiropoulos Phys. Rev. B 95, 165442 — Published 24 April 2017 DOI: 10.1103/PhysRevB.95.165442 Lattice Field Theory Study of Magnetic Catalysis in Graphene Carleton DeTar,1 Christopher Winterowd,1 and Savvas Zafeiropoulos2, 3, 4 1Department of Physics and Astronomy University of Utah, Salt Lake City, Utah 84112, USA 2Institut f¨urTheoretische Physik - Johann Wolfgang Goethe-Universit¨at Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany 3Jefferson Laboratory 12000 Jefferson Avenue, Newport News, Virginia 23606, USA 4Department of Physics College of William and Mary, Williamsburg, Virgina 23187-8795, USA (Dated: March 16, 2017) We discuss the simulation of the low-energy effective field theory (EFT) for graphene in the presence of an external magnetic field. -
CDT Quantum Toroidal Spacetimes: an Overview
universe Review CDT Quantum Toroidal Spacetimes: An Overview Jan Ambjorn 1,2,* , Zbigniew Drogosz 3 , Jakub Gizbert-Studnicki 3, Andrzej Görlich 3, Jerzy Jurkiewicz 3 and Dániel Nèmeth 3 1 The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark 2 Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands 3 Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, PL 30-348 Kraków, Poland; [email protected] (Z.D.); [email protected] (J.G.-S.); [email protected] (A.G.); [email protected] (J.J.); [email protected] (D.N.) * Correspondence: [email protected] Abstract: Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-independent in the spatial directions. The higher-order phase transitions observed in the model may be used to define a continuum limit of the lattice theory. Some aspects of the transitions are better studied when the topology of space is toroidal rather than spherical. In addition, a toroidal spatial topology allows us to understand more easily the nature of typical quantum fluctuations of the geometry. In particular, this topology makes it possible to use massless scalar fields that are solutions to Laplace’s equation with special boundary conditions as coordinates that capture the fractal structure of the quantum geometry. -
Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality
Symmetry, Integrability and Geometry: Methods and Applications SIGMA 13 (2017), 080, 22 pages Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality Vladimir A. FATEEV yz y Laboratoire Charles Coulomb UMR 5221 CNRS-UM2, Universit´ede Montpellier, 34095 Montpellier, France E-mail: [email protected] z Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia Received April 24, 2017, in final form October 03, 2017; Published online October 13, 2017 https://doi.org/10.3842/SIGMA.2017.080 Abstract. We study integrable deformations of sine-Liouville conformal field theory. Eve- ry integrable perturbation of this model is related to the series of quantum integrals of motion (hierarchy). We construct the factorized scattering matrices for different integrable perturbed conformal field theories. The perturbation theory, Bethe ansatz technique, renor- malization group and methods of perturbed conformal field theory are applied to show that all integrable deformations of sine-Liouville model possess non-trivial duality properties. Key words: integrability; duality; Ricci flow 2010 Mathematics Subject Classification: 16T25; 17B68; 83C47 1 Introduction Duality plays an important role in the analysis of statistical, quantum field and string theory systems. Usually it maps a weak coupling region of one theory to the strong coupling region of the other and makes it possible to use perturbative, semiclassical and renormalization group methods in different regions of the coupling constant. For example, the well known duality between sine-Gordon and massive Thirring models [7, 31] together with integrability plays an important role for the justification of exact scattering matrix [39] in these theories. Another well known example of the duality in two-dimensional integrable systems is the weak-strong cou- pling flow from affine Toda theories to the same theories with dual affine Lie algebra [2,6,9]. -
Quantum Computing for QCD?
Quantum Computing for QCD? Yannick Meurice The University of Iowa [email protected] With Alexei Bazavov, Sam Foreman, Erik Gustafson, Yuzhi Liu, Philipp Preiss, Shan-Wen Tsai, Judah Unmuth-Yockey, Li-Ping Yang, Johannes Zeiher, and Jin Zhang Supported by the Department of Energy USQCD, BNL, 4/27/19 Yannick Meurice (U. of Iowa) Quantum Computing for QCD? USQCD, BNL, 4/27/19 1 / 56 Content of the talk Quantum Computing (QC) for QCD: what do we want to do? Strategy: big goals with enough intermediate steps explore as many paths as possible leave room for serendipity Tensor tools: QC friends and competitors (RG) Quantum simulations experiments (analog): cold atoms, ions ... Quantum computations (digital): IBM, IonQ, Rigetti, ... Abelian Higgs model with cold atom ladders Benchmark for real time scattering (arXiv:1901.05944, PRD in press with Erik Gustafson and Judah Unmuth-Yockey) Symmetry preserving truncations (YM, arxiv:1903.01918) Quantum Joule experiments (arXiv:1903.01414, with Jin Zhang and Shan-Wen Tsai) Pitch for a quantum center for theoretical physics (HEP, NP, ...) Conclusions Yannick Meurice (U. of Iowa) Quantum Computing for QCD? USQCD, BNL, 4/27/19 2 / 56 Computing with quantum devices (Feynman 82)? The number of transistors on a chip doubled almost every two years for more than 30 years At some point, the miniaturization involves quantum mechanics Capacitors are smaller but they are still on (charged) or off (uncharged) Figure: Moore’s law, source: qubits: jΨi = αj0i + βj1i is a Wikipedia superposition of the two possibilities. Can we use quantum devices to explore large Hilbert spaces? Yes, if the interactions are localized (generalization of Trotter product Figure: Quantum circuit for the formula, Lloyd 96) quantum Ising model (E. -
Current Definition and Mass Renormalization in a Model Field Theory
IC/67/24 INTERNATIONAL ATOMIC ENERGY AGENCY INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS CURRENT DEFINITION AND MASS RENORMALIZATION IN A MODEL FIELD THEORY C. R. HAGEN 1967 PIAZZA OBERDAN TRIESTE IC/67/24 INTERNATIONAL ATOMIC ENERGY AdENCY INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS CURRENT DEFINITION AND MASS HEJTORMALIZATION BT A MODEL FIELD THEORY * C.R. Hagen ** TRIESTE April 1967 *To be Bubmitted to "Nuovo Cimento" **On leave of absenoe from the Univereiiy of Rochester,NY, USA ABSTRACT It is demonstrated that a field theory of vector mesons inter- acting with massless fermions in a world of one spatial dimension has an infinite number of solutions in direot analogy to the case of the Thirring model. Each of these solutions corresponds to a different value of a certain parameter £ whioh enters into the definition of the ourrent operator of the theory. The physical mass of the veotor meson is shown to depend linearly upon this parameter attaining its bare value u, for the exceptional oase in which the pseudo-vector current is exactly conserved. The limits jA-o —> °o and JLLQ -» 0 are examined, the former yielding results previously obtained for the Thirring model while the latter implies a unique value for ^ and defines the radiation gauge formulation of Schwinger's two-dimensional model of electrodynamics. -1- CURRENT DEFINITION AND MASS RENORMALIZATION IN A MODEL FIELD THEORY 1. VECTOR MSSOITS IN ONE SPATIAL DIMENSION Although the soluble relativistic models known at the present time are remarkably few in number, they have long been cherished by field theorists for their value as potential testing areas for new techniques in particle physics.