=
|
|
- Opal Wilcox
- 5 years ago
- Views:
Transcription
1 = x 3 4
2 Application of DMRG to 2D systems L y L x Unit cell Periodic boundary conditions for both x and y directions k y = 2n/L y = X n / l 2 Initial basis states (Landau gauge) (r) = exp [ i X n y (x X n ) 2 XN l 2l ] H ( x X n ) 2 2 N l One particle states are uniquely specified by X n and N H N : Hermite polynomials X n : guiding center N : Landau level index Mapping on to effective D lattice model D lattice model Xn
3 Density matrix renormalization Ground state ij i > j > i j Density matrix ii' =j ij * i'j Norm Tr Ground state energy (Ne=) DMRG m= m= m= m= N=2 =/2 Exact Eigenvalues of N= =/3 Ne=8 M = i
4 Ground state of quantum Hall systems Type-II stripe Stripe II FQHE N= WC Fermi liquid N= Stripe II Stripe I Laughlin state N=2 WC Bubble Stripe I Wigner crystal Bubble Type-I stripe
5 Fractional quantum Hall effect R. Willett et al (987) Hall resistance Longitudinal resistance
6 N=2 Landau level Stripe state =3/7 E G 3-stripes 2-stripes (b) 4-stripes (a) (c) L x /L y (a) L x /L y =.3 (b) L x /L y =.8 (c) L x /L y =2.3 x x x y y y
7 Ground state of N=2 Landau level N Wigner crystal Two-electron bubble state Type I stripe state Shibata and Yoshioka: Phys. Rev. Lett (2)
8 Stripe and bubble states 3 g(,y) 2 stripe I Wigner crystal /7 /6 /5 =2/9 /3 /4 3/ 4/ 2/5 /2 3/7 2-electron bubble y 9/2 Lilly et al. (999) Two-electron bubble state Type I stripe state DMRG WC 2-electron bubble stripe I y Hartree-Fock x electron bubble
9 Effective interaction in higher Landau levels Pure Coulomb Potential energy generated by the two electrons separated by x x = 5 Veff N= N= N= Veff (x) + Veff (xx) Veff (x) N=2 N=3 2Rc N= r N= Veff (xx) x 4 Veff (x) + Veff (xx) Rc : cyclotron radius e 2Rc e Veff (x) Rc e Veff (xx) x x = 5 4 e
10 Entanglement entropy Wave function S=/2 2-Spin system S S2 S = or S2 = or SS2 S > S2 > Reduced density matrix Entanglement entropy S is independent of S2 - Not correlated - ( > > ) SS2 = > S ( > > ) S2 disentangled S depends on S2 - correlated - ( > > ) Singlet state entangled
11 Scaling of entanglement entropy D system Short range correlation : L D-XXZ model ( L >> correlation length ) 2 gapless Power law correlation : (D critical system ) gapfull L
12 Scaling of entanglement entropy Short range correlation ( L >> ) entanglement D-dimensional system Area law L boundary size (length) Topological order in 2D Non-trivial universal correction Boundary term Topological term Fractional quantum Hall state = /m Laughlin state : D = m /2
13 Torus geometry Density matrix eigenvalues i Fractional quantum Hall state = /3 i. Ne=8 Ne= Ne=2 torus. Ne : electron number Lx Ly. boundary i
14 Entanglement entropy Torus geometry Fractional quantum Hall state = /3 Pair correlation functions =/3 4 Ne = 8 ~6 Ly / l = 7.4 Ly / l = 6.2 x/l Ly / l = 5. 3 Ly / l = 3.7 ( boundary length ) Ly / l = torus Lx Ly boundary Lx / l
15 Entanglement entropy 6 Entanglement entropy =/3 fractional quantum Hall state boundary term topological term sphere 4 2 topological entropy sphere N= 6 22 N= torus spherical : ln m /2 torus : 2 ln m /2 sphere ln 3 /2 ~.55 torus 2ln 3 /2 ~ =/m topological term L: boundary length torus L / l : boundary length L: boundary length
16 6 4 2 topological entropy 2 Entanglement entropy Fractional quantum Hall state topological term spherical : ln m /2 torus : 2 ln m /2 ( =/m ) Entanglement entropy boundary term =/5 sphere N=8 =/3 torus =/3 sphere 2 24 sphere ln 3/2 ~.55 ln 5 /2 ~ L / l : boundary length topological term torus 2ln 3/2 ~. sphere L: boundary length torus L: boundary length
17 f ( x) 2 sin x L f ( x) sin 2 x L x L A. Gendiar, R. Krcmar, and T. Nishino, Prog. Theor. Phys. 22, 953 (29); 23, 393 (2).
18 H ( )c Original k k k / 2 L k c k L 2 f ( x) sin x L f ( x) sin 2 kx / 2 coskx 2 exp 2 4 k 2 L ikx exp ikx H Deform k k k ( k ( ( ) c k k 2 k k 2 k c k ) c ) c k k k c c k k k H Deform T. Hikihara and T. Nishino, Phys. Rev. B 83, 644(R) (2) H. Katsura, J. Phys. A 44, 252 (2)
19 Naokazu Shibata and Daijiro Yoshioka: Phys. Rev. Lett (2) Shibata and Hotta: Phys. Rev. B (2) Hotta and Shibata: Phys. Rev. B 86 48(R) (22)
20 E E - F x L x L
21 S=/2 Heisenberg spin ladder.578. E/L J / J =. H =. M S=/2 spin ladder J J J J / J = /L H E/L.59 J / J =. H =.8 M /L 3.3 H =.6 x J / J =. 6
22 Nishimoto, Shibata and Hotta: Nature Communications (23)
23
24
25 .52.5 = Ne=49 Ne=48 2 x 3 4 7/9 M 5/9 3/9 /9 2 3 H
Sine square deformation(ssd) and Mobius quantization of 2D CFTs
riken_ssd_2017 arxiv:1603.09543/ptep(2016) 063A02 Sine square deformation(ssd) and Mobius quantization of 2D CFTs Niigata University, Kouichi Okunishi Related works: Kastura, Ishibashi Tada, Wen Ryu Ludwig
More informationSine square deformation(ssd)
YITP arxiv:1603.09543 Sine square deformation(ssd) and Mobius quantization of twodimensional conformal field theory Niigata University, Kouichi Okunishi thanks Hosho Katsura(Univ. Tokyo) Tsukasa Tada(RIKEN)
More informationZooming in on the Quantum Hall Effect
Zooming in on the Quantum Hall Effect Cristiane MORAIS SMITH Institute for Theoretical Physics, Utrecht University, The Netherlands Capri Spring School p.1/31 Experimental Motivation Historical Summary:
More informationSine Square Deformatin (SSD) of 1d critical systems (and others)
Sine Square Deformatin (SSD) of 1d critical systems (and others) Shinsei Ryu Univ. of Chicago In collaboration with Xueda Wen (MIT) and Andreas Ludwig (UCSB) Inhomogenous systems - Inhomogenous systems
More informationThe Quantum Hall Effects
The Quantum Hall Effects Integer and Fractional Michael Adler July 1, 2010 1 / 20 Outline 1 Introduction Experiment Prerequisites 2 Integer Quantum Hall Effect Quantization of Conductance Edge States 3
More informationSine-Square Deformation (SSD) and its Relevance to String Theory
Sine-Square Deformation (SSD) and its Relevance to String Theory Tsukasa Tada Riken Nishina Center Based on work with N. Ishibashi! and [arxiv:1404.6343] Conformal Field Theory in 2 dim. Let us consider
More informationEntanglement in Topological Phases
Entanglement in Topological Phases Dylan Liu August 31, 2012 Abstract In this report, the research conducted on entanglement in topological phases is detailed and summarized. This includes background developed
More informationMomentum-space and Hybrid Real- Momentum Space DMRG applied to the Hubbard Model
Momentum-space and Hybrid Real- Momentum Space DMRG applied to the Hubbard Model Örs Legeza Reinhard M. Noack Collaborators Georg Ehlers Jeno Sólyom Gergely Barcza Steven R. White Collaborators Georg Ehlers
More informationGapless Spin Liquids in Two Dimensions
Gapless Spin Liquids in Two Dimensions MPA Fisher (with O. Motrunich, Donna Sheng, Matt Block) Boulder Summerschool 7/20/10 Interest Quantum Phases of 2d electrons (spins) with emergent rather than broken
More informationMatrix product states for the fractional quantum Hall effect
Matrix product states for the fractional quantum Hall effect Roger Mong (California Institute of Technology) University of Virginia Feb 24, 2014 Collaborators Michael Zaletel UC Berkeley (Stanford/Station
More informationQuantum numbers and collective phases of composite fermions
Quantum numbers and collective phases of composite fermions Quantum numbers Effective magnetic field Mass Magnetic moment Charge Statistics Fermi wave vector Vorticity (vortex charge) Effective magnetic
More informationQuantum Spin-Metals in Weak Mott Insulators
Quantum Spin-Metals in Weak Mott Insulators MPA Fisher (with O. Motrunich, Donna Sheng, Simon Trebst) Quantum Critical Phenomena conference Toronto 9/27/08 Quantum Spin-metals - spin liquids with Bose
More informationDetecting signatures of topological order from microscopic Hamiltonians
Detecting signatures of topological order from microscopic Hamiltonians Frank Pollmann Max Planck Institute for the Physics of Complex Systems FTPI, Minneapolis, May 2nd 2015 Detecting signatures of topological
More informationMagnetic Crystals and Helical Liquids in Alkaline-Earth 1D Fermionic Gases
Magnetic Crystals and Helical Liquids in Alkaline-Earth 1D Fermionic Gases Leonardo Mazza Scuola Normale Superiore, Pisa Seattle March 24, 2015 Leonardo Mazza (SNS) Exotic Phases in Alkaline-Earth Fermi
More informationPreface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
More informationTopological Kondo Insulator SmB 6. Tetsuya Takimoto
Topological Kondo Insulator SmB 6 J. Phys. Soc. Jpn. 80 123720, (2011). Tetsuya Takimoto Department of Physics, Hanyang University Collaborator: Ki-Hoon Lee (POSTECH) Content 1. Introduction of SmB 6 in-gap
More informationMPS formulation of quasi-particle wave functions
MPS formulation of quasi-particle wave functions Eddy Ardonne Hans Hansson Jonas Kjäll Jérôme Dubail Maria Hermanns Nicolas Regnault GAQHE-Köln 2015-12-17 Outline Short review of matrix product states
More informationLecture 3: Tensor Product Ansatz
Lecture 3: Tensor Product nsatz Graduate Lectures Dr Gunnar Möller Cavendish Laboratory, University of Cambridge slide credits: Philippe Corboz (ETH / msterdam) January 2014 Cavendish Laboratory Part I:
More informationLes états de bord d un. isolant de Hall atomique
Les états de bord d un isolant de Hall atomique séminaire Atomes Froids 2/9/22 Nathan Goldman (ULB), Jérôme Beugnon and Fabrice Gerbier Outline Quantum Hall effect : bulk Landau levels and edge states
More informationNematic Order and Geometry in Fractional Quantum Hall Fluids
Nematic Order and Geometry in Fractional Quantum Hall Fluids Eduardo Fradkin Department of Physics and Institute for Condensed Matter Theory University of Illinois, Urbana, Illinois, USA Joint Condensed
More informationCondensed matter theory Lecture notes and problem sets 2012/2013
Condensed matter theory Lecture notes and problem sets 2012/2013 Dmitri Ivanov Recommended books and lecture notes: [AM] N. W. Ashcroft and N. D. Mermin, Solid State Physics. [Mar] M. P. Marder, Condensed
More informationPhases of strongly-interacting bosons on a two-leg ladder
Phases of strongly-interacting bosons on a two-leg ladder Marie Piraud Arnold Sommerfeld Center for Theoretical Physics, LMU, Munich April 20, 2015 M. Piraud Phases of strongly-interacting bosons on a
More informationMagnets, 1D quantum system, and quantum Phase transitions
134 Phys620.nb 10 Magnets, 1D quantum system, and quantum Phase transitions In 1D, fermions can be mapped into bosons, and vice versa. 10.1. magnetization and frustrated magnets (in any dimensions) Consider
More informationShunsuke Furukawa Condensed Matter Theory Lab., RIKEN. Gregoire Misguich Vincent Pasquier Service de Physique Theorique, CEA Saclay, France
Shunsuke Furukawa Condensed Matter Theory Lab., RIKEN in collaboration with Gregoire Misguich Vincent Pasquier Service de Physique Theorique, CEA Saclay, France : ground state of the total system Reduced
More informationLecture 2 2D Electrons in Excited Landau Levels
Lecture 2 2D Electrons in Excited Landau Levels What is the Ground State of an Electron Gas? lower density Wigner Two Dimensional Electrons at High Magnetic Fields E Landau levels N=2 N=1 N= Hartree-Fock
More informationBeyond the Quantum Hall Effect
Beyond the Quantum Hall Effect Jim Eisenstein California Institute of Technology School on Low Dimensional Nanoscopic Systems Harish-chandra Research Institute January February 2008 Outline of the Lectures
More informationQuantum Order: a Quantum Entanglement of Many Particles
Quantum Order: a Quantum Entanglement of Many Particles Xiao-Gang Wen Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Dated: Sept. 2001) It is pointed out
More informationTOPMAT CEA & CNRS, Saclay, France June 14, Inti Sodemann MPI - PKS Dresden
TOPMAT 2018 CEA & CNRS, Saclay, France June 14, 2018 Inti Sodemann MPI - PKS Dresden Part I New phase transitions of Composite Fermions Part II Bosonization and shear sound in 2D Fermi liquids New phase
More informationJournal of Theoretical Physics
1 Journal of Theoretical Physics Founded and Edited by M. Apostol 53 (2000) ISSN 1453-4428 Ionization potential for metallic clusters L. C. Cune and M. Apostol Department of Theoretical Physics, Institute
More informationTechniques for translationally invariant matrix product states
Techniques for translationally invariant matrix product states Ian McCulloch University of Queensland Centre for Engineered Quantum Systems (EQuS) 7 Dec 2017 Ian McCulloch (UQ) imps 7 Dec 2017 1 / 33 Outline
More informationSpectrum of Holographic Wilson Loops
Spectrum of Holographic Wilson Loops Leopoldo Pando Zayas University of Michigan Continuous Advances in QCD 2011 University of Minnesota Based on arxiv:1101.5145 Alberto Faraggi and LPZ Work in Progress,
More informationQuantum phase transitions in condensed matter physics, with connections to string theory
Quantum phase transitions in condensed matter physics, with connections to string theory sachdev.physics.harvard.edu HARVARD High temperature superconductors Cuprates High temperature superconductors Pnictides
More informationProbing Wigner Crystals in the 2DEG using Microwaves
Probing Wigner Crystals in the 2DEG using Microwaves G. Steele CMX Journal Club Talk 9 September 2003 Based on work from the groups of: L. W. Engel (NHMFL), D. C. Tsui (Princeton), and collaborators. CMX
More informationOrbital magnetic field effects in spin liquid with spinon Fermi sea: Possible application to (ET)2Cu2(CN)3
Orbital magnetic field effects in spin liquid with spinon Fermi sea: Possible application to (ET)2Cu2(CN)3 Olexei Motrunich (KITP) PRB 72, 045105 (2005); PRB 73, 155115 (2006) with many thanks to T.Senthil
More informationRenormalization of Tensor Network States
Renormalization of Tensor Network States I. Coarse Graining Tensor Renormalization Tao Xiang Institute of Physics Chinese Academy of Sciences txiang@iphy.ac.cn Numerical Renormalization Group brief introduction
More informationIntoduction to topological order and topologial quantum computation. Arnau Riera, Grup QIC, Dept. ECM, UB 16 de maig de 2009
Intoduction to topological order and topologial quantum computation Arnau Riera, Grup QIC, Dept. ECM, UB 16 de maig de 2009 Outline 1. Introduction: phase transitions and order. 2. The Landau symmetry
More informationFrom Particles to Fields
From Particles to Fields Tien-Tsan Shieh Institute of Mathematics Academic Sinica July 25, 2011 Tien-Tsan Shieh (Institute of MathematicsAcademic Sinica) From Particles to Fields July 25, 2011 1 / 24 Hamiltonian
More informationQuantification of Entanglement Entropies for Doubly Excited States in Helium
Quantification of Entanglement Entropies for Doubly Excited States in Helium Chien-Hao Lin and Yew Kam Ho Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan March 6 th, 2015 Abstract
More informationEntanglement Chern numbers for random systems
POSTECH, Korea, July 31 (2015) Ψ = 1 D D Entanglement Chern numbers for random systems j Ψ j Ψj Yasuhiro Hatsugai Institute of Physics, Univ. of Tsukuba Ref: T. Fukui & Y. Hatsugai, J. Phys. Soc. Jpn.
More informationExact results concerning the phase diagram of the Hubbard Model
Steve Kivelson Apr 15, 2011 Freedman Symposium Exact results concerning the phase diagram of the Hubbard Model S.Raghu, D.J. Scalapino, Li Liu, E. Berg H. Yao, W-F. Tsai, A. Lauchli G. Karakonstantakis,
More informationRecent results in microwave and rf spectroscopy of two-dimensional electron solids
J. Phys. IV France 131 (2005) 241 245 C EDP Sciences, Les Ulis DOI: 10.1051/jp4:2005131061 Recent results in microwave and rf spectroscopy of two-dimensional electron solids R.M. Lewis 1,2, Y.P. Chen 1,2,
More informationNew Physics in High Landau Levels
New Physics in High Landau Levels J.P. Eisenstein 1, M.P. Lilly 1, K.B. Cooper 1, L.N. Pfeiffer 2 and K.W. West 2 1 California Institute of Technology, Pasadena, CA 91125 2 Bell Laboratories, Lucent Technologies,
More informationTensor network methods in condensed matter physics. ISSP, University of Tokyo, Tsuyoshi Okubo
Tensor network methods in condensed matter physics ISSP, University of Tokyo, Tsuyoshi Okubo Contents Possible target of tensor network methods! Tensor network methods! Tensor network states as ground
More informationSpherical Deformation for One-dimensional Quantum Systems
1 Spherical Deformation for One-dimensional Quantum Systems Andrej Gendiar 1,, Roman Krcmar 1, and Tomotoshi ishino,3 arxiv:0810.06v [cond-mat.str-el] 30 Mar 009 1 Institute of Electrical Engineering,
More informationThe density matrix renormalization group and tensor network methods
The density matrix renormalization group and tensor network methods Outline Steve White Exploiting the low entanglement of ground states Matrix product states and DMRG 1D 2D Tensor network states Some
More informationCorrelated 2D Electron Aspects of the Quantum Hall Effect
Correlated 2D Electron Aspects of the Quantum Hall Effect Magnetic field spectrum of the correlated 2D electron system: Electron interactions lead to a range of manifestations 10? = 4? = 2 Resistance (arb.
More informationQuantum Entanglement in Exactly Solvable Models
Quantum Entanglement in Exactly Solvable Models Hosho Katsura Department of Applied Physics, University of Tokyo Collaborators: Takaaki Hirano (U. Tokyo Sony), Yasuyuki Hatsuda (U. Tokyo) Prof. Yasuhiro
More informationGraduate Quantum Mechanics I: Prelims and Solutions (Fall 2015)
Graduate Quantum Mechanics I: Prelims and Solutions (Fall 015 Problem 1 (0 points Suppose A and B are two two-level systems represented by the Pauli-matrices σx A,B σ x = ( 0 1 ;σ 1 0 y = ( ( 0 i 1 0 ;σ
More informationThe Density Matrix Renormalization Group: Introduction and Overview
The Density Matrix Renormalization Group: Introduction and Overview Introduction to DMRG as a low entanglement approximation Entanglement Matrix Product States Minimizing the energy and DMRG sweeping The
More informationBraid Group, Gauge Invariance and Topological Order
Braid Group, Gauge Invariance and Topological Order Yong-Shi Wu Department of Physics University of Utah Topological Quantum Computing IPAM, UCLA; March 2, 2007 Outline Motivation: Topological Matter (Phases)
More informationEntanglement signatures of QED3 in the kagome spin liquid. William Witczak-Krempa
Entanglement signatures of QED3 in the kagome spin liquid William Witczak-Krempa Aspen, March 2018 Chronologically: X. Chen, KITP Santa Barbara T. Faulkner, UIUC E. Fradkin, UIUC S. Whitsitt, Harvard S.
More informationEfficient time evolution of one-dimensional quantum systems
Efficient time evolution of one-dimensional quantum systems Frank Pollmann Max-Planck-Institut für komplexer Systeme, Dresden, Germany Sep. 5, 2012 Hsinchu Problems we will address... Finding ground states
More informationFermionic tensor networks
Fermionic tensor networks Philippe Corboz, Institute for Theoretical Physics, ETH Zurich Bosons vs Fermions P. Corboz and G. Vidal, Phys. Rev. B 80, 165129 (2009) : fermionic 2D MERA P. Corboz, R. Orus,
More informationFrustration without competition: the SU(N) model of quantum permutations on a lattice
Frustration without competition: the SU(N) model of quantum permutations on a lattice F. Mila Ecole Polytechnique Fédérale de Lausanne Switzerland Collaborators P. Corboz (Zürich), A. Läuchli (Innsbruck),
More informationTopology of electronic bands and Topological Order
Topology of electronic bands and Topological Order R. Shankar The Institute of Mathematical Sciences, Chennai TIFR, 26 th April, 2011 Outline IQHE and the Chern Invariant Topological insulators and the
More informationENERGY BAND STRUCTURE OF ALUMINIUM BY THE AUGMENTED PLANE WAVE METHOD
ENERGY BAND STRUCTURE OF ALUMINIUM BY THE AUGMENTED PLANE WAVE METHOD L. SMR6KA Institute of Solid State Physics, Czeehosl. Acad. Sci., Prague*) The band structure of metallic aluminium has been calculated
More informationNew Phases of Two-Dimensional Electrons in Excited Landau Levels
i New Phases of Two-Dimensional Electrons in Excited Landau Levels Thesis by Ken B. Cooper In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology
More information5 Topological defects and textures in ordered media
5 Topological defects and textures in ordered media In this chapter we consider how to classify topological defects and textures in ordered media. We give here only a very short account of the method following
More informationGolden chain of strongly interacting Rydberg atoms
Golden chain of strongly interacting Rydberg atoms Hosho Katsura (Gakushuin Univ.) Acknowledgment: Igor Lesanovsky (MUARC/Nottingham Univ. I. Lesanovsky & H.K., [arxiv:1204.0903] Outline 1. Introduction
More informationarxiv: v2 [quant-ph] 12 Aug 2008
Complexity of thermal states in quantum spin chains arxiv:85.449v [quant-ph] Aug 8 Marko Žnidarič, Tomaž Prosen and Iztok Pižorn Department of physics, FMF, University of Ljubljana, Jadranska 9, SI- Ljubljana,
More informationParamagnetic phases of Kagome lattice quantum Ising models p.1/16
Paramagnetic phases of Kagome lattice quantum Ising models Predrag Nikolić In collaboration with T. Senthil Massachusetts Institute of Technology Paramagnetic phases of Kagome lattice quantum Ising models
More information1 Supplementary Figure
Supplementary Figure Tunneling conductance ns.5..5..5 a n =... B = T B = T. - -5 - -5 5 Sample bias mv E n mev 5-5 - -5 5-5 - -5 4 n 8 4 8 nb / T / b T T 9T 8T 7T 6T 5T 4T Figure S: Landau-level spectra
More informationKitaev honeycomb lattice model: from A to B and beyond
Kitaev honeycomb lattice model: from A to B and beyond Jiri Vala Department of Mathematical Physics National University of Ireland at Maynooth Postdoc: PhD students: Collaborators: Graham Kells Ahmet Bolukbasi
More informationImpurity corrections to the thermodynamics in spin chains using a transfer-matrix DMRG method
PHYSICAL REVIEW B VOLUME 59, NUMBER 9 1 MARCH 1999-I Impurity corrections to the thermodynamics in spin chains using a transfer-matrix DMRG method Stefan Rommer and Sebastian Eggert Institute of Theoretical
More informationIt from Qubit Summer School
It from Qubit Summer School July 27 th, 2016 Tensor Networks Guifre Vidal NSERC Wednesday 27 th 9AM ecture Tensor Networks 2:30PM Problem session 5PM Focus ecture MARKUS HAURU MERA: a tensor network for
More informationGlobal phase diagrams of two-dimensional quantum antiferromagnets. Subir Sachdev Harvard University
Global phase diagrams of two-dimensional quantum antiferromagnets Cenke Xu Yang Qi Subir Sachdev Harvard University Outline 1. Review of experiments Phases of the S=1/2 antiferromagnet on the anisotropic
More informationTopological Insulators
Topological Insulators Aira Furusai (Condensed Matter Theory Lab.) = topological insulators (3d and 2d) Outline Introduction: band theory Example of topological insulators: integer quantum Hall effect
More information1. Possible Spin Liquid States on the Triangular and Kagomé Lattices, Kun Yang, L. K. Warman and S. M. Girvin, Phys. Rev. Lett. 70, 2641 (1993).
Publications of Kun Yang 1. Possible Spin Liquid States on the Triangular and Kagomé Lattices, Kun Yang, L. K. Warman and S. M. Girvin, Phys. Rev. Lett. 70, 2641 (1993). 2. Quantum Ferromagnetism and Phase
More informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son GGI conference Gauge/gravity duality 2015 Ref.: 1502.03446 Plan Plan Fractional quantum Hall effect Plan Fractional quantum Hall effect Composite fermion
More informationEntanglement in Many-Body Fermion Systems
Entanglement in Many-Body Fermion Systems Michelle Storms 1, 2 1 Department of Physics, University of California Davis, CA 95616, USA 2 Department of Physics and Astronomy, Ohio Wesleyan University, Delaware,
More informationHaldane phase and magnetic end-states in 1D topological Kondo insulators. Alejandro M. Lobos Instituto de Fisica Rosario (IFIR) - CONICET- Argentina
Haldane phase and magnetic end-states in 1D topological Kondo insulators Alejandro M. Lobos Instituto de Fisica Rosario (IFIR) - CONICET- Argentina Workshop on Next Generation Quantum Materials ICTP-SAIFR,
More informationCorrelated 2D Electron Aspects of the Quantum Hall Effect
Correlated 2D Electron Aspects of the Quantum Hall Effect Outline: I. Introduction: materials, transport, Hall effects II. III. IV. Composite particles FQHE, statistical transformations Quasiparticle charge
More informationSmall and large Fermi surfaces in metals with local moments
Small and large Fermi surfaces in metals with local moments T. Senthil (MIT) Subir Sachdev Matthias Vojta (Augsburg) cond-mat/0209144 Transparencies online at http://pantheon.yale.edu/~subir Luttinger
More informationPhysics Qual - Statistical Mechanics ( Fall 2016) I. Describe what is meant by: (a) A quasi-static process (b) The second law of thermodynamics (c) A throttling process and the function that is conserved
More informationMP464: Solid State Physics Problem Sheet
MP464: Solid State Physics Problem Sheet 1 Write down primitive lattice vectors for the -dimensional rectangular lattice, with sides a and b in the x and y-directions respectively, and a face-centred rectangular
More information2D Electrostatics and the Density of Quantum Fluids
2D Electrostatics and the Density of Quantum Fluids Jakob Yngvason, University of Vienna with Elliott H. Lieb, Princeton University and Nicolas Rougerie, University of Grenoble Yerevan, September 5, 2016
More informationEfficient Representation of Ground States of Many-body Quantum Systems: Matrix-Product Projected States Ansatz
Efficient Representation of Ground States of Many-body Quantum Systems: Matrix-Product Projected States Ansatz Systematic! Fermionic! D>1?! Chung-Pin Chou 1, Frank Pollmann 2, Ting-Kuo Lee 1 1 Institute
More informationFermionic partial transpose fermionic entanglement and fermionic SPT phases
Fermionic partial transpose fermionic entanglement and fermionic SPT phases Shinsei Ryu University of Chicago November 7, 2017 Outline 1. Bosonic case (Haldane chain) What is partial tranpose? Why it is
More informationBose Description of Pauli Spin Operators and Related Coherent States
Commun. Theor. Phys. (Beijing, China) 43 (5) pp. 7 c International Academic Publishers Vol. 43, No., January 5, 5 Bose Description of Pauli Spin Operators and Related Coherent States JIANG Nian-Quan,,
More informationNon-Abelian Statistics. in the Fractional Quantum Hall States * X. G. Wen. School of Natural Sciences. Institute of Advanced Study
IASSNS-HEP-90/70 Sep. 1990 Non-Abelian Statistics in the Fractional Quantum Hall States * X. G. Wen School of Natural Sciences Institute of Advanced Study Princeton, NJ 08540 ABSTRACT: The Fractional Quantum
More informationElectron-electron interactions and Dirac liquid behavior in graphene bilayers
Electron-electron interactions and Dirac liquid behavior in graphene bilayers arxiv:85.35 S. Viola Kusminskiy, D. K. Campbell, A. H. Castro Neto Boston University Workshop on Correlations and Coherence
More informationPhysics of graphene. Hideo Aoki Univ Tokyo, Japan. Yasuhiro Hatsugai Univ Tokyo / Tsukuba, Japan Takahiro Fukui Ibaraki Univ, Japan
Physics of graphene Hideo Aoki Univ Tokyo, Japan Yasuhiro Hatsugai Univ Tokyo / Tsukuba, Japan Takahiro Fukui Ibaraki Univ, Japan Purpose Graphene a atomically clean monolayer system with unusual ( massless
More informationFermi liquid & Non- Fermi liquids. Sung- Sik Lee McMaster University Perimeter Ins>tute
Fermi liquid & Non- Fermi liquids Sung- Sik Lee McMaster University Perimeter Ins>tute Goal of many- body physics : to extract a small set of useful informa>on out of a large number of degrees of freedom
More informationAdvanced Computation for Complex Materials
Advanced Computation for Complex Materials Computational Progress is brainpower limited, not machine limited Algorithms Physics Major progress in algorithms Quantum Monte Carlo Density Matrix Renormalization
More informationThermodynamics of quantum Heisenberg spin chains
PHYSICAL REVIEW B VOLUME 58, NUMBER 14 Thermodynamics of quantum Heisenberg spin chains 1 OCTOBER 1998-II Tao Xiang Research Centre in Superconductivity, University of Cambridge, Madingley Road, Cambridge
More informationQUANTUM MECHANICS. Franz Schwabl. Translated by Ronald Kates. ff Springer
Franz Schwabl QUANTUM MECHANICS Translated by Ronald Kates Second Revised Edition With 122Figures, 16Tables, Numerous Worked Examples, and 126 Problems ff Springer Contents 1. Historical and Experimental
More informationThe uses of Instantons for classifying Topological Phases
The uses of Instantons for classifying Topological Phases - anomaly-free and chiral fermions Juven Wang, Xiao-Gang Wen (arxiv:1307.7480, arxiv:140?.????) MIT/Perimeter Inst. 2014 @ APS March A Lattice
More informationν=0 Quantum Hall state in Bilayer graphene: collective modes
ν= Quantum Hall state in Bilayer graphene: collective modes Bilayer graphene: Band structure Quantum Hall effect ν= state: Phase diagram Time-dependent Hartree-Fock approximation Neutral collective excitations
More informationarxiv: v1 [cond-mat.other] 20 Apr 2010
Characterization of 3d topological insulators by 2d invariants Rahul Roy Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, UK arxiv:1004.3507v1 [cond-mat.other] 20 Apr 2010
More informationTopological Insulators and Superconductors
Topological Insulators and Superconductors Lecture #1: Topology and Band Theory Lecture #: Topological Insulators in and 3 dimensions Lecture #3: Topological Superconductors, Majorana Fermions an Topological
More informationOrganizing Principles for Understanding Matter
Organizing Principles for Understanding Matter Symmetry Conceptual simplification Conservation laws Distinguish phases of matter by pattern of broken symmetries Topology Properties insensitive to smooth
More informationLuttinger Liquid at the Edge of a Graphene Vacuum
Luttinger Liquid at the Edge of a Graphene Vacuum H.A. Fertig, Indiana University Luis Brey, CSIC, Madrid I. Introduction: Graphene Edge States (Non-Interacting) II. III. Quantum Hall Ferromagnetism and
More informationQuantum phase transitions and entanglement in (quasi)1d spin and electron models
Quantum phase transitions and entanglement in (quasi)1d spin and electron models Elisa Ercolessi - Università di Bologna Group in Bologna: G.Morandi, F.Ortolani, E.E., C.Degli Esposti Boschi, A.Anfossi
More informationAlgebras, Representations and Quant Title. Approaches from mathematical scienc. Mechanical and Macroscopic Systems)
Algebras, Representations and Quant Title Approaches from mathematical scienc information, Chaos and Nonlinear Dy Mechanical and Macroscopic Systems) Author(s) Tanimura, Shogo Citation 物性研究 (2005), 84(3):
More informationI. PLATEAU TRANSITION AS CRITICAL POINT. A. Scaling flow diagram
1 I. PLATEAU TRANSITION AS CRITICAL POINT The IQHE plateau transitions are examples of quantum critical points. What sort of theoretical description should we look for? Recall Anton Andreev s lectures,
More informationGROUND - STATE ENERGY OF CHARGED ANYON GASES
GROUD - STATE EERGY OF CHARGED AYO GASES B. Abdullaev, Institute of Applied Physics, ational University of Uzbekistan. 4.09.013 APUAG FU Berlin 1 Contents Interacting anyons in D harmonic potential in
More information1 Superfluidity and Bose Einstein Condensate
Physics 223b Lecture 4 Caltech, 04/11/18 1 Superfluidity and Bose Einstein Condensate 1.6 Superfluid phase: topological defect Besides such smooth gapless excitations, superfluid can also support a very
More informationTopological Kondo Insulators!
Topological Kondo Insulators! Maxim Dzero, University of Maryland Collaborators: Kai Sun, University of Maryland Victor Galitski, University of Maryland Piers Coleman, Rutgers University Main idea Kondo
More informationarxiv:cond-mat/ v1 [cond-mat.mes-hall] 12 Mar 1997
Light scattering from a periodically modulated two dimensional arxiv:cond-mat/9703119v1 [cond-mat.mes-hall] 12 Mar 1997 electron gas with partially filled Landau levels Arne Brataas 1 and C. Zhang 2 and
More informationSymmetry, Topology and Phases of Matter
Symmetry, Topology and Phases of Matter E E k=λ a k=λ b k=λ a k=λ b Topological Phases of Matter Many examples of topological band phenomena States adiabatically connected to independent electrons: - Quantum
More information