Supersymmetry in strongly correlated fermion models
|
|
- Geoffrey Stanley
- 5 years ago
- Views:
Transcription
1 Supersymmetry in strongly correlated fermion models Dimitrios Galanakis () Stefanos Papanikolaou (2) Chris Henley (3) () Nanyang Technological University (Singapore) (2) Yale University (3) Cornell University
2 Hard-core spinless fermions on a lattice Nearest neighbor exclusion Square Lattice Hubbard model 4 N Spinless nn excluded fermions 2 N/2 2
3 Supersymmetric Lattice Hamiltonian Creation operator of hard-core nn excluded fermions where: d i c i P i,excl P i,excl ( c j c j) <j,i> If we define: Q i d i a natural form of Hamiltonian is: H {Q,Q} <ij> d i d j + i P i,excl [H, Q] H, Q Fendley and Schoutens 5 Q 2 (Q ) 2 Supersymmetry ψ> and Q ψ> are degenerate 3
4 Zero energy states re may be eigenstates: Q ψ > Q ψ > zero energy states allow for a very large degeneracy (even exponential) of groundstate. Triangular lattice super-frustration. This may be root to exotic phases. 4
5 Computational methods Lanczos diagonalization (via ARPACK) Periodic clusters of arbitrary shape (3-45 sites) Momentum resolution 5
6 Range of zero energy states Jonsson () conjectured that cross-cycles are zero energy states (Electr. J. Comb., 6(2):#R5, 29) For triangular lattice /5 > f > /7 Interesting physics arises at boundaries of this interval 6
7 Energy vs filling.7 45 Ground state energy per site appears like phase coexistence Filling 7
8 Entropy vs filling.25!"#$ N3...4!"#$%%%&$ N4...45!"&'%%%&(.2!"#.,/23 Entropy.5!"%$.!"%.5!"!$!.!"%.2!"%#.4!"%&.6!"%'.8!"%(.2!"#.22!"##.25!"#$ )*++*,- Filling 8
9 Clusters with a zero energy state at f>/5 (9,3)x(,4)33 (8,4)x(3,7)44 (7,4)x(2,6)34 (,)x(,4)43 (3,4)x(2,4)44 (,)x(,4)44 (2,2)x(2,4)44 (9,2)x(,4)34 (,2)x(,4)38 9
10 reference fermion ( origin); zero occupancy being ne origin. Black is max. occupancy, dark and light gray are 2nd 3rd highest occ.; I didn t tryand distingush lightest sites from figurei was sent Isotropic cluster (8,4)x(3,7), f9/44 Density - Density correlation 5 usual transverse hops Abacus order layer 6 layer 5 2 inter column hops from a pair to a new pair order destroying hop: pair new pair (after this hop)
11 8% which an approximate state containing only twosuggest low energy components: form for ground state containing only Triangular lattice, K, 3-4 sites two low energy components: (n) (2 column) (n ) Triangular lattice, K, 3-4 sites Ψ s,.9 a ψa Ψa (n) sa ψa(2 column) Ψ(n ), a,2 Ψ a Stripes in (2n,)x(,5) ladders, f/5 density-density where sa is For coefficient of Schmidt decomposi n2,3,4,5 and filling2n (n ) where sa is coefficient of Schmidt decomposition. It turns out that Ψ feature a nearly iden,2 correlation Unique zero energy state (n ) a,2 tion. It turns that feature a nearly idenψ titical entanglement which allows for,2this prostripes inout d-d correlation spectrum, cedure to be carried out entanglement iteratively for spectrum, remaining of allows for this protitical which.4 Factorizable wave function system, which cedure gives a to leading contribution form be carried out iteratively for remaining of.3 system, which gives a leading contribution form n n 2 (i) (i).2 (n) (i) (i) Φ + λ, Ψ Φ + λφ3 Φ3 n + n 2 2 (n) (i) (i) (i) (i). i i + λ Φ3 +, Ψ Φ Φ2 + λ Φ i i Filling where.35 i,..., n is index of a double column and Filling where double column and,..., n is index 2 of a i(i) te energy of KCM momen Φ2 S (i) lar lattice. Because of superfrustra S : ground state energy of KCM momen2 Φ(i) (i) triangular lattice is varies little Φ S Φ S 2 tor for triangular lattice. Because of superfrustra d size for a given filling. We observe (i) ground state of triangular lattice is varies little S for.4 < v <.22. Φ e cluster shape and size for a given filling. We observe (i) ergy ground states for.4 < v <.22. Φ S 2 (i) (i) ty-density corellation profile,nn () n (x), nsity-density corellation profile, () n (x), S S 3S S Φ3 Φ to unique zero energy state for 5 unique zero energy state for 5 (6,)x(,5) (i) boundary conditions for /5 andand profile, n () n (x), Φ S Figure 2:conditions density-density corellation S cdic boundary forfilling fillingofof /5 3 In this graphical representation that corresponds to unique zero energy state for 5 this graphical representation nearest nearest h site are 4 nearest sites toger with ladder with periodic boundary conditions for filling of /5 and te are 4 nearest sites toger with (i) where S is a symmetrization operator which performs (8,)x(,5) lower corellation left diagonal neighbors. numbers nsity profile, n ()graphical n (x), symmetrizes S operator Φ3 nearest along column where S is S asymmetrization which performs for Kdiagonal In this representation CM.neighbors. wer left numbers a circular perumutation of indices along v (, 5). coloring schemestate is such site zero is unique zero energy for that 5 indices along v (, 5). neighbors of each site are 4 nearest sites toger with a circular perumutation of endary coloring scheme is such that site zero is parameter λ ( λ / for is a variational d or sites are where S 6 5) conditions for colored filling ofaccoring /5 andto is a operator which perfo upper right and lower left diagonal numbers parameter / forsymmetrization is a variational or sites are colored accoring to neighbors. parameter. (x), such that darker indicates higher values. For 6λ (5λladder overlap of6 5) this wave graphical representation nearest circular perumutation are site coloring scheme is such thatwith site ground zero nearest neighbor exclusion, all with neighbors function statea6is about 88.9%., such thatlabels. darker indicates higher values. parameter. Foris 5 ladder overlap of of this indices wave along v ( 4 nearest sites toger parameter λ (88.9%. λ / for 6 5) is a variatio where S accoring is a symmetrization operator which performs pty. However rest of system forms colored white and or are colored to ft diagonal neighbors. numbers rest neighbor exclusion, all sites neighbors overlap of this approximate function with function with ground state iswave about.5
12 Conclusions Strong evidence for systematic violation of bound set by Johnson on triangular lattice, reporting zero energy and supersymmetric states for f>.5 We report novel patterns for high filling zero energy states f.5 and we propose idealized wavefunctions in order to understand novel quantum order. Glimpses of a phase transition at f~.5, possibly discontinuous 2
Many-Body Fermion Density Matrix: Operator-Based Truncation Scheme
Many-Body Fermion Density Matrix: Operator-Based Truncation Scheme SIEW-ANN CHEONG and C. L. HENLEY, LASSP, Cornell U March 25, 2004 Support: NSF grants DMR-9981744, DMR-0079992 The Big Picture GOAL Ground
More informationSupersymmetry, lattice fermions, independence complexes and cohomology theory
c 2010 International Press Adv. Theor. Math. Phys. 14 (2010) 643 694 Supersymmetry, lattice fermions, independence complexes and cohomology theory Liza Huijse 1,2 and Kareljan Schoutens 1 1 Institute for
More informationPhysics 239/139 Spring 2018 Assignment 2 Solutions
University of California at San Diego Department of Physics Prof. John McGreevy Physics 39/139 Spring 018 Assignment Solutions Due 1:30pm Monday, April 16, 018 1. Classical circuits brain-warmer. (a) Show
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 informationH ψ = E ψ. Introduction to Exact Diagonalization. Andreas Läuchli, New states of quantum matter MPI für Physik komplexer Systeme - Dresden
H ψ = E ψ Introduction to Exact Diagonalization Andreas Läuchli, New states of quantum matter MPI für Physik komplexer Systeme - Dresden http://www.pks.mpg.de/~aml laeuchli@comp-phys.org Simulations of
More information2D Bose and Non-Fermi Liquid Metals
2D Bose and Non-Fermi Liquid Metals MPA Fisher, with O. Motrunich, D. Sheng, E. Gull, S. Trebst, A. Feiguin KITP Cold Atoms Workshop 10/5/2010 Interest: A class of exotic gapless 2D Many-Body States a)
More informationAn ingenious mapping between integrable supersymmetric chains
An ingenious mapping between integrable supersymmetric chains Jan de Gier University of Melbourne Bernard Nienhuis 65th birthday, Amsterdam 2017 György Fehér Sasha Garbaly Kareljan Schoutens Jan de Gier
More informationThe Mott Metal-Insulator Transition
Florian Gebhard The Mott Metal-Insulator Transition Models and Methods With 38 Figures Springer 1. Metal Insulator Transitions 1 1.1 Classification of Metals and Insulators 2 1.1.1 Definition of Metal
More informationÖsszefonódás és felületi törvény 2. Szabad rácsmodellek
Összefonódás és felületi törvény 2. Szabad rácsmodellek Eisler Viktor MTA-ELTE Elméleti Fizikai Kutatócsoport Entanglement Day 2014.09.05. I. Peschel & V. Eisler, J. Phys. A: Math. Theor. 42, 504003 (2009)
More informationMajorana Fermions in Superconducting Chains
16 th December 2015 Majorana Fermions in Superconducting Chains Matilda Peruzzo Fermions (I) Quantum many-body theory: Fermions Bosons Fermions (II) Properties Pauli exclusion principle Fermions (II)
More informationApplication of the Lanczos Algorithm to Anderson Localization
Application of the Lanczos Algorithm to Anderson Localization Adam Anderson The University of Chicago UW REU 2009 Advisor: David Thouless Effect of Impurities in Materials Naively, one might expect that
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 informationTime-dependent DMRG:
The time-dependent DMRG and its applications Adrian Feiguin Time-dependent DMRG: ^ ^ ih Ψ( t) = 0 t t [ H ( t) E ] Ψ( )... In a truncated basis: t=3 τ t=4 τ t=5τ t=2 τ t= τ t=0 Hilbert space S.R.White
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 informationDepartment of Physics, Princeton University. Graduate Preliminary Examination Part II. Friday, May 10, :00 am - 12:00 noon
Department of Physics, Princeton University Graduate Preliminary Examination Part II Friday, May 10, 2013 9:00 am - 12:00 noon Answer TWO out of the THREE questions in Section A (Quantum Mechanics) and
More informationarxiv:quant-ph/ v2 24 Dec 2003
Quantum Entanglement in Heisenberg Antiferromagnets V. Subrahmanyam Department of Physics, Indian Institute of Technology, Kanpur, India. arxiv:quant-ph/0309004 v2 24 Dec 2003 Entanglement sharing among
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 informationGauge dynamics of kagome antiferromagnets. Michael J. Lawler (Binghamton University, Cornell University)
Gauge dynamics of kagome antiferromagnets Michael J. Lawler (Binghamton University, Cornell University) Outline Introduction to highly frustrated magnets Constrained spin models Dirac s generalized Hamiltonian
More informationAnderson Localization Looking Forward
Anderson Localization Looking Forward Boris Altshuler Physics Department, Columbia University Collaborations: Also Igor Aleiner Denis Basko, Gora Shlyapnikov, Vincent Michal, Vladimir Kravtsov, Lecture2
More informationNumerical diagonalization studies of quantum spin chains
PY 502, Computational Physics, Fall 2016 Anders W. Sandvik, Boston University Numerical diagonalization studies of quantum spin chains Introduction to computational studies of spin chains Using basis states
More informationMeasuring Entanglement Entropy in Valence Bond Quantum Monte Carlo Simulations
Measuring Entanglement Entropy in Valence Bond Quantum Monte Carlo Simulations by Ann Berlinsky Kallin A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the
More informationLuigi Paolasini
Luigi Paolasini paolasini@esrf.fr LECTURE 4: MAGNETIC INTERACTIONS - Dipole vs exchange magnetic interactions. - Direct and indirect exchange interactions. - Anisotropic exchange interactions. - Interplay
More information3 Symmetry Protected Topological Phase
Physics 3b Lecture 16 Caltech, 05/30/18 3 Symmetry Protected Topological Phase 3.1 Breakdown of noninteracting SPT phases with interaction Building on our previous discussion of the Majorana chain and
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 informationA New look at the Pseudogap Phase in the Cuprates.
A New look at the Pseudogap Phase in the Cuprates. Patrick Lee MIT Common themes: 1. Competing order. 2. superconducting fluctuations. 3. Spin gap: RVB. What is the elephant? My answer: All of the above!
More informationElectrons in a periodic potential
Chapter 3 Electrons in a periodic potential 3.1 Bloch s theorem. We consider in this chapter electrons under the influence of a static, periodic potential V (x), i.e. such that it fulfills V (x) = V (x
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 informationRandom Fermionic Systems
Random Fermionic Systems Fabio Cunden Anna Maltsev Francesco Mezzadri University of Bristol December 9, 2016 Maltsev (University of Bristol) Random Fermionic Systems December 9, 2016 1 / 27 Background
More informationSpin liquids in frustrated magnets
May 20, 2010 Contents 1 Frustration 2 3 4 Exotic excitations 5 Frustration The presence of competing forces that cannot be simultaneously satisfied. Heisenberg-Hamiltonian H = 1 J ij S i S j 2 ij The ground
More informationComputational strongly correlated materials R. Torsten Clay Physics & Astronomy
Computational strongly correlated materials R. Torsten Clay Physics & Astronomy Current/recent students Saurabh Dayal (current PhD student) Wasanthi De Silva (new grad student 212) Jeong-Pil Song (finished
More informationLecture 8 Nature of ensemble: Role of symmetry, interactions and other system conditions: Part II
Lecture 8 Nature of ensemble: Role of symmetry, interactions and other system conditions: Part II We continue our discussion of symmetries and their role in matrix representation in this lecture. An example
More informationThe Quantum Heisenberg Ferromagnet
The Quantum Heisenberg Ferromagnet Soon after Schrödinger discovered the wave equation of quantum mechanics, Heisenberg and Dirac developed the first successful quantum theory of ferromagnetism W. Heisenberg,
More informationQuantum Lattice Models & Introduction to Exact Diagonalization
Quantum Lattice Models & Introduction to Exact Diagonalization H! = E! Andreas Läuchli IRRMA EPF Lausanne ALPS User Workshop CSCS Manno, 28/9/2004 Outline of this lecture: Quantum Lattice Models Lattices
More informationWe can instead solve the problem algebraically by introducing up and down ladder operators b + and b
Physics 17c: Statistical Mechanics Second Quantization Ladder Operators in the SHO It is useful to first review the use of ladder operators in the simple harmonic oscillator. Here I present the bare bones
More informationMultipartite entanglement in fermionic systems via a geometric
Multipartite entanglement in fermionic systems via a geometric measure Department of Physics University of Pune Pune - 411007 International Workshop on Quantum Information HRI Allahabad February 2012 In
More informationLinked-Cluster Expansions for Quantum Many-Body Systems
Linked-Cluster Expansions for Quantum Many-Body Systems Boulder Summer School 2010 Simon Trebst Lecture overview Why series expansions? Linked-cluster expansions From Taylor expansions to linked-cluster
More informationQuantum spin systems - models and computational methods
Summer School on Computational Statistical Physics August 4-11, 2010, NCCU, Taipei, Taiwan Quantum spin systems - models and computational methods Anders W. Sandvik, Boston University Lecture outline Introduction
More informationquasi-particle pictures from continuous unitary transformations
quasi-particle pictures from continuous unitary transformations Kai Phillip Schmidt 24.02.2016 quasi-particle pictures from continuous unitary transformations overview Entanglement in Strongly Correlated
More informationMany-Body Localization. Geoffrey Ji
Many-Body Localization Geoffrey Ji Outline Aside: Quantum thermalization; ETH Single-particle (Anderson) localization Many-body localization Some phenomenology (l-bit model) Numerics & Experiments Thermalization
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 informationLecture 6. Fermion Pairing. WS2010/11: Introduction to Nuclear and Particle Physics
Lecture 6 Fermion Pairing WS2010/11: Introduction to Nuclear and Particle Physics Experimental indications for Cooper-Pairing Solid state physics: Pairing of electrons near the Fermi surface with antiparallel
More informationStrongly correlated systems in atomic and condensed matter physics. Lecture notes for Physics 284 by Eugene Demler Harvard University
Strongly correlated systems in atomic and condensed matter physics Lecture notes for Physics 284 by Eugene Demler Harvard University September 18, 2014 2 Chapter 5 Atoms in optical lattices Optical lattices
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 informationStripes and holes in a two-dimensional model of spinless fermions or hardcore bosons
PHYSICAL REVIEW B 68, 014506 2003 Stripes and holes in a two-dimensional model of spinless fermions or hardcore bosons N. G. Zhang* and C. L. Henley Department of Physics, Cornell University, Ithaca, New
More informationTime Evolving Block Decimation Algorithm
Time Evolving Block Decimation Algorithm Application to bosons on a lattice Jakub Zakrzewski Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University,
More informationMOMENTUM DISTRIBUTION OF ITINERANT ELECTRONS IN THE ONE-DIMENSIONAL FALICOV KIMBALL MODEL
International Journal of Modern Physics B Vol. 17, No. 27 (23) 4897 4911 c World Scientific Publishing Company MOMENTUM DISTRIBUTION OF ITINERANT EECTRONS IN THE ONE-DIMENSIONA FAICOV KIMBA MODE PAVO FARKAŠOVSKÝ
More informationSimulations of Quantum Dimer Models
Simulations of Quantum Dimer Models Didier Poilblanc Laboratoire de Physique Théorique CNRS & Université de Toulouse 1 A wide range of applications Disordered frustrated quantum magnets Correlated fermions
More informationTensor network simulations of strongly correlated quantum systems
CENTRE FOR QUANTUM TECHNOLOGIES NATIONAL UNIVERSITY OF SINGAPORE AND CLARENDON LABORATORY UNIVERSITY OF OXFORD Tensor network simulations of strongly correlated quantum systems Stephen Clark LXXT[[[GSQPEFS\EGYOEGXMZMXMIWUYERXYQGSYVWI
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 informationarxiv: v1 [quant-ph] 8 Sep 2010
Few-Body Systems, (8) Few- Body Systems c by Springer-Verlag 8 Printed in Austria arxiv:9.48v [quant-ph] 8 Sep Two-boson Correlations in Various One-dimensional Traps A. Okopińska, P. Kościk Institute
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 informationJACOBI S ITERATION METHOD
ITERATION METHODS These are methods which compute a sequence of progressively accurate iterates to approximate the solution of Ax = b. We need such methods for solving many large linear systems. Sometimes
More informationarxiv:quant-ph/ v5 10 Feb 2003
Quantum entanglement of identical particles Yu Shi Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom and Theory of
More informationPHYSICAL REVIEW B 80,
PHYSICAL REVIEW B 8, 6526 29 Finite-temperature exact diagonalization cluster dynamical mean-field study of the two-dimensional Hubbard model: Pseudogap, non-fermi-liquid behavior, and particle-hole asymmetry
More informationTopological insulator with time-reversal symmetry
Phys620.nb 101 7 Topological insulator with time-reversal symmetry Q: Can we get a topological insulator that preserves the time-reversal symmetry? A: Yes, with the help of the spin degree of freedom.
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 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 informationSolutions Final exam 633
Solutions Final exam 633 S.J. van Enk (Dated: June 9, 2008) (1) [25 points] You have a source that produces pairs of spin-1/2 particles. With probability p they are in the singlet state, ( )/ 2, and with
More informationPerturbation Theory 1
Perturbation Theory 1 1 Expansion of Complete System Let s take a look of an expansion for the function in terms of the complete system : (1) In general, this expansion is possible for any complete set.
More information4 Matrix product states
Physics 3b Lecture 5 Caltech, 05//7 4 Matrix product states Matrix product state (MPS) is a highly useful tool in the study of interacting quantum systems in one dimension, both analytically and numerically.
More informationIntroduction to Supersymmetric Quantum Mechanics and Lattice Regularization
Introduction to Supersymmetric Quantum Mechanics and Lattice Regularization Christian Wozar Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz, 07743 Jena, Germany
More informationQuantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings
Quantum numbers for relative ground states of antiferromagnetic Heisenberg spin rings Klaus Bärwinkel, Peter Hage, Heinz-Jürgen Schmidt, and Jürgen Schnack Universität Osnabrück, Fachbereich Physik, D-49069
More informationSupersymmetry breaking and Nambu-Goldstone fermions in lattice models
YKIS2016@YITP (2016/6/15) Supersymmetry breaking and Nambu-Goldstone fermions in lattice models Hosho Katsura (Department of Physics, UTokyo) Collaborators: Yu Nakayama (IPMU Rikkyo) Noriaki Sannomiya
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 informationRenormalization of Tensor- Network States Tao Xiang
Renormalization of Tensor- Network States Tao Xiang Institute of Physics/Institute of Theoretical Physics Chinese Academy of Sciences txiang@iphy.ac.cn Physical Background: characteristic energy scales
More informationLS coupling. 2 2 n + H s o + H h f + H B. (1) 2m
LS coupling 1 The big picture We start from the Hamiltonian of an atomic system: H = [ ] 2 2 n Ze2 1 + 1 e 2 1 + H s o + H h f + H B. (1) 2m n e 4πɛ 0 r n 2 4πɛ 0 r nm n,m Here n runs pver the electrons,
More informationScaling analysis of snapshot spectra in the world-line quantum Monte Carlo for the transverse-field Ising chain
TNSAA 2018-2019 Dec. 3-6, 2018, Kobe, Japan Scaling analysis of snapshot spectra in the world-line quantum Monte Carlo for the transverse-field Ising chain Kouichi Seki, Kouichi Okunishi Niigata University,
More informationAntiferromagnetic order in the Hubbard Model on the Penrose Lattice
Antiferromagnetic order in the Hubbard Model on the Penrose Lattice Akihisa Koga Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo -8, Japan Hirokazu Tsunetsugu The Institute for Solid
More informationLecture 10: Solving the Time-Independent Schrödinger Equation. 1 Stationary States 1. 2 Solving for Energy Eigenstates 3
Contents Lecture 1: Solving the Time-Independent Schrödinger Equation B. Zwiebach March 14, 16 1 Stationary States 1 Solving for Energy Eigenstates 3 3 Free particle on a circle. 6 1 Stationary States
More informationarxiv: v2 [cond-mat.str-el] 14 Sep 2011
Geometrical frustration effects on charge-driven quantum phase transitions arxiv:116.8v [cond-mat.str-el] 1 Sep 11 L. Cano-Cortés, 1 A. Ralko, C. Février, J. Merino, 1 and S. Fratini 1 Departamento de
More informationThree-body Interactions in Cold Polar Molecules
Three-body Interactions in Cold Polar Molecules H.P. Büchler Theoretische Physik, Universität Innsbruck, Austria Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften,
More informationThe Dirac Equation. Topic 3 Spinors, Fermion Fields, Dirac Fields Lecture 13
The Dirac Equation Dirac s discovery of a relativistic wave equation for the electron was published in 1928 soon after the concept of intrisic spin angular momentum was proposed by Goudsmit and Uhlenbeck
More informationDegeneracy Breaking in Some Frustrated Magnets. Bangalore Mott Conference, July 2006
Degeneracy Breaking in Some Frustrated Magnets Doron Bergman Greg Fiete Ryuichi Shindou Simon Trebst UCSB Physics KITP UCSB Physics Q Station Bangalore Mott Conference, July 2006 Outline Motivation: Why
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 informationMatrix Product States
Matrix Product States Ian McCulloch University of Queensland Centre for Engineered Quantum Systems 28 August 2017 Hilbert space (Hilbert) space is big. Really big. You just won t believe how vastly, hugely,
More informationSemigroup Quantum Spin Chains
Semigroup Quantum Spin Chains Pramod Padmanabhan Center for Physics of Complex Systems Institute for Basic Science, Korea 12th July, 2018 Based on work done with D. Texeira, D. Trancanelli ; F. Sugino
More informationQuantum Mechanics Solutions. λ i λ j v j v j v i v i.
Quantum Mechanics Solutions 1. (a) If H has an orthonormal basis consisting of the eigenvectors { v i } of A with eigenvalues λ i C, then A can be written in terms of its spectral decomposition as A =
More information1 Quantum field theory and Green s function
1 Quantum field theory and Green s function Condensed matter physics studies systems with large numbers of identical particles (e.g. electrons, phonons, photons) at finite temperature. Quantum field theory
More informationLecture 5. Hartree-Fock Theory. WS2010/11: Introduction to Nuclear and Particle Physics
Lecture 5 Hartree-Fock Theory WS2010/11: Introduction to Nuclear and Particle Physics Particle-number representation: General formalism The simplest starting point for a many-body state is a system of
More informationDimer model implementations of quantum loop gases. C. Herdman, J. DuBois, J. Korsbakken, K. B. Whaley UC Berkeley
Dimer model implementations of quantum loop gases C. Herdman, J. DuBois, J. Korsbakken, K. B. Whaley UC Berkeley Outline d-isotopic quantum loop gases and dimer model implementations generalized RK points
More informationGeneral Exam Part II, Fall 1998 Quantum Mechanics Solutions
General Exam Part II, Fall 1998 Quantum Mechanics Solutions Leo C. Stein Problem 1 Consider a particle of charge q and mass m confined to the x-y plane and subject to a harmonic oscillator potential V
More informationInteraction-induced Symmetry Protected Topological Phase in Harper-Hofstadter models
Interaction-induced Symmetry Protected Topological Phase in Harper-Hofstadter models arxiv:1609.03760 Lode Pollet Dario Hügel Hugo Strand, Philipp Werner (Uni Fribourg) Algorithmic developments diagrammatic
More informationarxiv:cond-mat/ v2 [cond-mat.str-el] 24 Feb 2006
Applications of Cluster Perturbation Theory Using Quantum Monte Carlo Data arxiv:cond-mat/0512406v2 [cond-mat.str-el] 24 Feb 2006 Fei Lin, Erik S. Sørensen, Catherine Kallin and A. John Berlinsky Department
More informationQuantum dynamics in ultracold atoms
Rather don t use Power-Points title Page Use my ypage one instead Quantum dynamics in ultracold atoms Corinna Kollath (Ecole Polytechnique Paris, France) T. Giamarchi (University of Geneva) A. Läuchli
More informationNon-magnetic states. The Néel states are product states; φ N a. , E ij = 3J ij /4 2 The Néel states have higher energy (expectations; not eigenstates)
Non-magnetic states Two spins, i and j, in isolation, H ij = J ijsi S j = J ij [Si z Sj z + 1 2 (S+ i S j + S i S+ j )] For Jij>0 the ground state is the singlet; φ s ij = i j i j, E ij = 3J ij /4 2 The
More informationGiant Enhancement of Quantum Decoherence by Frustrated Environments
ISSN 0021-3640, JETP Letters, 2006, Vol. 84, No. 2, pp. 99 103. Pleiades Publishing, Inc., 2006.. Giant Enhancement of Quantum Decoherence by Frustrated Environments S. Yuan a, M. I. Katsnelson b, and
More informationarxiv: v1 [cond-mat.quant-gas] 18 Sep 2015
Slightly imbalanced system of a few attractive fermions in a one-dimensional harmonic trap Tomasz Sowiński arxiv:1509.05515v1 [cond-mat.quant-gas] 18 Sep 2015 Institute of Physics of the Polish Academy
More informationDilute limit of a strongly-interacting model of spinless fermions and hardcore bosons on the square lattice
Eur. Phys. J. B 38, 409 430 (2004) DOI: 10.1140/epjb/e2004-00135-8 THE EUROPEA PHYSICAL JOURAL B Dilute limit of a strongly-interacting model of spinless fermions and hardcore bosons on the square lattice.g.
More informationSpin liquids on ladders and in 2d
Spin liquids on ladders and in 2d MPA Fisher (with O. Motrunich) Minnesota, FTPI, 5/3/08 Interest: Quantum Spin liquid phases of 2d Mott insulators Background: Three classes of 2d Spin liquids a) Topological
More informationSupersymmetric Quantum Mechanics and Geometry by Nicholas Mee of Trinity College, Cambridge. October 1989
Supersymmetric Quantum Mechanics and Geometry by Nicholas Mee of Trinity College Cambridge October 1989 Preface This dissertation is the result of my own individual effort except where reference is explicitly
More informationIdentical Particles in Quantum Mechanics
Identical Particles in Quantum Mechanics Chapter 20 P. J. Grandinetti Chem. 4300 Nov 17, 2017 P. J. Grandinetti (Chem. 4300) Identical Particles in Quantum Mechanics Nov 17, 2017 1 / 20 Wolfgang Pauli
More informationTime-Independent Perturbation Theory
4 Phys46.nb Time-Independent Perturbation Theory.. Overview... General question Assuming that we have a Hamiltonian, H = H + λ H (.) where λ is a very small real number. The eigenstates of the Hamiltonian
More informationUnderstanding the complete temperature-pressure phase diagrams of organic charge-transfer solids
Understanding the complete temperature-pressure phase diagrams of organic charge-transfer solids Collaborators: R. Torsten Clay Department of Physics & Astronomy HPC 2 Center for Computational Sciences
More informationThe 1+1-dimensional Ising model
Chapter 4 The 1+1-dimensional Ising model The 1+1-dimensional Ising model is one of the most important models in statistical mechanics. It is an interacting system, and behaves accordingly. Yet for a variety
More informationQFT. Unit 1: Relativistic Quantum Mechanics
QFT Unit 1: Relativistic Quantum Mechanics What s QFT? Relativity deals with things that are fast Quantum mechanics deals with things that are small QFT deals with things that are both small and fast What
More informationEmergent spin. Michael Creutz BNL. On a lattice no relativity can consider spinless fermions hopping around
Emergent spin Michael Creutz BNL Introduction quantum mechanics + relativity spin statistics connection fermions have half integer spin On a lattice no relativity can consider spinless fermions hopping
More informationProblem Set No. 1: Quantization of Non-Relativistic Fermi Systems Due Date: September 14, Second Quantization of an Elastic Solid
Physics 56, Fall Semester 5 Professor Eduardo Fradkin Problem Set No. : Quantization of Non-Relativistic Fermi Systems Due Date: September 4, 5 Second Quantization of an Elastic Solid Consider a three-dimensional
More informationDegeneracy Breaking in Some Frustrated Magnets
Degeneracy Breaking in Some Frustrated Magnets Doron Bergman Greg Fiete Ryuichi Shindou Simon Trebst UCSB Physics KITP UCSB Physics Q Station cond-mat: 0510202 (prl) 0511176 (prb) 0605467 0607210 0608131
More informationNext topic: Quantum Field Theories for Quantum Many-Particle Systems; or "Second Quantization"
Next topic: Quantum Field Theories for Quantum Many-Particle Systems; or "Second Quantization" Outline 1 Bosons and Fermions 2 N-particle wave functions ("first quantization" 3 The method of quantized
More informationDephasing, relaxation and thermalization in one-dimensional quantum systems
Dephasing, relaxation and thermalization in one-dimensional quantum systems Fachbereich Physik, TU Kaiserslautern 26.7.2012 Outline 1 Introduction 2 Dephasing, relaxation and thermalization 3 Particle
More information