Andreas Kreisel. Institut für Theoretische Physik Johann Wolfgang Goethe Universität Frankfurt am Main. July,

Size: px
Start display at page:

Download "Andreas Kreisel. Institut für Theoretische Physik Johann Wolfgang Goethe Universität Frankfurt am Main. July,"

Transcription

1 BEC of magnons and spin wave interactions in QAF Andreas Kreisel Institut für Theoretische Physik Johann Wolfgang Goethe Universität Frankfurt am Main July, collaborators: N. Hasselmann, P. Kopietz

2 Interacting bosons T=0 Bogoliubov theory (1947) euclidean action for interacting Bose gas S[ ¹ª; ª] = S 2 [ ¹ª; ª] + S 4 [ ¹ª; ª] Z S 2 [ ª; ¹ ª] = ( i! + ² k ¹) ª ¹ K ª K S 4 [ ª; ¹ ª] = K Z Z 1 (2!) 2 ± K1 +K 2 ;K 3 +K 4 V (fk i g) ª ¹ K1 ªK2 ¹ ª K3 ª K4 K 1 K 4 Bogoliubov shift ª K = ª 0 K + ª K ª 0 K = ± K;0 p ½0 h ª k i = 0 ) ~ S ¹ ª; ª = N. Bogoliubov (1947) 4X i=0 ~S i ¹ ª; ª

3 Goldstone bosons constraint to chemical potential (minimum) ~S 1 ¹ ª; ª = 0 diagonalization q E k = ² 2 k + 2½ 0U(k)² k = c 0 jkj + jkj 3 + O(k 5 ) condensate density ½ 0 = ¹ U(0) gapless excitations: velocity c 0 = r ¹ m

4 Heisenberg ferromagnet Spin waves in Heisenbergmagnets Holstein-Primakoff transformation around classical ground state S i = p r 2Sb y i 1 n i 2S = (S+ i )y n i = b Si z = S n i bosonic hamiltonian ^H = 1 2 X J ij S i S j J ij = J < 0 ij y i b i ; h i b y i ; b j = ± ij H = E cl + H 2 + H 4 + O(b 6 ) E cl = NS[2DJS h] H 2 = S X J ij ³n i + n j + b y i 2 b j b y j b i + h X ij i H 4 = 1 X ³ J ij 2n i n j b y i 4 n ib j b y j n ib j ij N. Hasselmann, P. Kopietz, Europhys. Lett. 74, 1067 (2006) n i

5 BEC of Holstein-Primakoff bosons in ferromagnets? FT: diagonalizes quadratic part b i = p 1 X e ik r i b k N k E k = ~ J 0 S(1 k k = X ± ~J 0 = 2DJ e ik ± H 2 = X k E k b y k b k interaction vanishes: to weak interaction of ferromagnetic spin waves H 4 = 1 X ± k1 +k 2V 2 ;k 3 +k 4 V (fk i g) b y k 1 b y k 2 b k3 b k4 k 1 k 4 V (fk i g)» k 1 k 2 + k 3 k 4 + O(k 4 ) no BEC!

6 ^H = 1 2 Heisenberg antiferromagnet X J ij S i S j J ij = J > 0 ij conventional spin wave expansion transformations Holstein-Primakoff H = E cl + H 2 + H 4 + O(b 6 ) E cl = DNJS 2 H 2 = S X J ij ³b y i b i + b y j b j + b i b j + b y i by j ij Fourier transformation using reduced BZ r r 2 X b i = e ik r i 2 X A k b i = e ik r i B k N N k diagonalization: Bogoliubov transformation µ µ µ Ak uk v B y = k k ² k = p 1 k 2 k v k u k y k k = 1 DX cos(k i a) D Anderson (1952), Kubo (1952), Oguchi (1960) k i=1

7 Spin-wave interactions 2 degenerate magnon modes H 2 = X ³ E k y k k + y k k E 0 k E k = ~ J 0 S² k spin-wave interactions: complicated H 4 = 1 X ³ 4V Â 0 k 1 k 4 V (1) 1234 interaction vertices s V (1) 1234» 1 jk 1 jjk 2 j 2 jk 3 jjk 4 j y 1 y y 3 y : : : µ 1 + k 1 k 2 jk 1 jjk 2 j but: all divergences cancel in physical quantities infrared singular in some limits N. Hasselmann, P. Kopietz, Europhys. Lett. 74, 1067 (2006)

8 BEC of magnons in QAF quantum antiferromagnet in magnetic field h = g¹ B B ^H = 1 X J ij S i S j h X has U(1) symmetry Si z rotational symmetry 2 ij i around magnetic field classical ground states I. h = 0 II. h < h c = 2 ~ J 0 S III. h > h c A. Kreisel, N. Hasselmann, and P. Kopietz, Phys. Rev. Lett. 98, (2007)

9 Formulation in terms of 2 Transformations magnons Holstein-Primakoff (fluctuations around FM ground state) S i = p r 2Sb y i 1 n i 2S = h i (S+ i )y y n i = bi b i ; b y i ; b j = ± ij Si z = S n i H = E cl + H 2 + H 4 + O(b 6 ) fourier transformation: red. BZ (2 Modes) H 2 = X k;¾= (² k¾ ¹) b y k¾ b k¾ ² k = k2 2m + O(k4 ) ² k+ = h c + O(k 2 ) h c = 2 ~ J 0 S

10 Continuum formulation neglect gapped mode for simplicity ª k = p Na D b k interacting bosonic fields H = Z d D k (2¼) D µ k 2 2m ¹ ª y k ª k Z k Z k 0 Z q U q ª y k+ q ªy k 0 q ª k 0 ª k effective interaction: constant for small momenta U q = ( 0 jqj)â 1 0 Â 0 = 1 2 ~J 0 a D m = 1 2JSa 2

11 Hermitian parametrization hermitian operators k = y k k = y k [ k ; q ] = i(2¼) D ±(k q) transformation: split up field r s ª k = 2 µ k + p i k 2sµ s = S a D transverse longitudinal advantage: physical interpretation of operators k» X i k» X i ³ i e ik r i S x i ³ i e ik r i S y i ³ i = h = he z ½ 1 i 2 A 1 i 2 B P. W. Anderson (1952) N. Hasselmann, P. Kopietz, Europhys. Lett. 74, 1067 (2006)

12 Symmetry breaking impose nonzero expectation value k = k + (2¼) D ±(k)á 0 H = E 0 + H 1 + H 2 + H 3 + H 4 fix chemical potential ¹ = U 0sÁ 0 2 diagonalization: Bogoliubov transformation H 2 = 1 Z d D k ³ 2 (2¼) ² D k y k k + y k k + E 0 r ¹ ² k = c 0 jkj + jkj 3 + O(k 5 ) c 0 = m = 1 8 p m 3 ¹

13 Quasiparticle decay decay in two or more quasiparticles energy conservation momentum conservation E k = E k1 + E k2 k = k 1 + k 2 consider energy dispersion E k = c 0 jkj + jk 3 + O(k 5 ) stable quasiparticles > 0 unstable quasiparticles concerning spontaneous decay < 0 M. E. Zhitormirsky, A. L. Chernyshev, Phys. Rev. Lett. 82, 4536 (1999)

14 Correlation functions hermitian fields ª k = r s 2 µ k + i p 2sµ k transverse correlations in gaussian approximation (linear spinwave theory)  1 0 h K K 0i = ± K; K 0! 2 + c 2 0 k2! h K K 0i = ± K; K 0! 2 + c 2 0 k2 h K K 0i = ± K; K 0 C. Castellani, C. Di Castro, F. Pistolesi, and G. C. Strinati, Phys. Rev. Lett. 78, 1612 (1997) F. Pistolesi, C. Castellani, C. Di Castro, and G. C. Strinati, Phys. Rev. B 69, (2004) K = (!; k) longitudinal  0 c 2 0k 2! 2 + c 0 k 2 quantitatively wrong in gaussian approximation

15 Beyond Bogoliubov divergences in pertubation theory (contribution to anomal Propagator) cancellations controlled by Ward identities due to U(1) - symmetry (2 correlations correct) critical continuum in longitudinal correlation function h K K i = Z 2 k contribution cancels in physical quantities of the Bose gas! 2! 2 + c 2 k 2 + K (mc) 3 D+1 Z½ 2½ 0 observable? Yes, BEC of magnons! fields: staggered magnetization 8 >< >: ln 2 3 D h (mc) 2! 2 =c 2 +k 2 i h i D 3! 2 c + k D = 3 1 < D < 3

16 Possible measurement neutron scattering might detect anomalous dimension in correlation function longitudinal 2 staggered structure factor 3 S k (k;!) = Âs2 M 2 s 4 Z2 k 2 cjkj ± (! cjkj) + C D(mc) 2 (! cjkj) 5 Z½½ 3 3 D! 2 0 c k2 2 2 critical continuum! only valid at (Ginzburg-scale) c k G

17 Restrictions Ginzburg-scale! c k G 2 contributions to abnormal propagator symmetry breaking divergent diagrams k G ¼ (mc)3 ½ 0 ¼ 4p 2 Sa µ» µ D = 2 k G ¼ mc e ½ 0 (mc) 3 ¼ p 3 S a µe 6 p 3µ D = 3 energy integrated structure factor spectral weight I ± : ± -function I critical continuum ³ c : ¼ k G k jkj ln G jkj D = 2 I c I ± I c I ± ¼ (mc)2 ½ 0 k G jkj D = 3

18 Summary not-so-well known facts about the Bose gas large corrections to Bogoliubov approximation in 1 < D 3 Spin-wave interactions in QAF interaction vertices: divergent (usual spin-wave expansion) hermitian field parametrization weak interactions between Goldstone modes fields: physical quantities QAF in uniform magnetic field: BEC of magnons measurable quantities via neutron scattering but only at D=2

Bose Einstein condensation of magnons and spin wave interactions in quantum antiferromagnets

Bose Einstein condensation of magnons and spin wave interactions in quantum antiferromagnets Bose Einstein condensation of magnons and spin wave interactions in quantum antiferromagnets Talk at Rutherford Appleton Lab, March 13, 2007 Peter Kopietz, Universität Frankfurt collaborators: Nils Hasselmann,

More information

Dynamic properties of interacting bosons and magnons

Dynamic properties of interacting bosons and magnons Ultracold Quantum Gases beyond Equilibrium Natal, Brasil, September 27 October 1, 2010 Dynamic properties of interacting bosons and magnons Peter Kopietz, Universität Frankfurt collaboration: A. Kreisel,

More information

Magnetic ordering of local moments

Magnetic ordering of local moments Magnetic ordering Types of magnetic structure Ground state of the Heisenberg ferromagnet and antiferromagnet Spin wave High temperature susceptibility Mean field theory Magnetic ordering of local moments

More information

Non-equilibrium time evolution of bosons from the functional renormalization group

Non-equilibrium time evolution of bosons from the functional renormalization group March 14, 2013, Condensed Matter Journal Club University of Florida at Gainesville Non-equilibrium time evolution of bosons from the functional renormalization group Peter Kopietz, Universität Frankfurt

More information

Theory Seminar Uni Marburg. Bose-Einstein Condensation and correlations in magnon systems

Theory Seminar Uni Marburg. Bose-Einstein Condensation and correlations in magnon systems Theory Seminar Uni Marburg 11 November, 2010 Bose-Einstein Condensation and correlations in magnon systems Peter Kopietz, Universität Frankfurt 1.) Bose-Einstein condensation 2.) Interacting magnons in

More information

Persistent spin current in a spin ring

Persistent spin current in a spin ring Persistent spin current in a spin ring Ming-Che Chang Dept of Physics Taiwan Normal Univ Jing-Nuo Wu (NCTU) Min-Fong Yang (Tunghai U.) A brief history precursor: Hund, Ann. Phys. 1934 spin charge persistent

More information

The Quantum Heisenberg Ferromagnet

The 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 information

Andreas Kreisel. University of Florida, Gainesville, FL. Bosons: Spin-waves and BEC in thin-film ferromagnets spin-wave theory interactions and BEC

Andreas Kreisel. University of Florida, Gainesville, FL. Bosons: Spin-waves and BEC in thin-film ferromagnets spin-wave theory interactions and BEC Andreas Kreisel University of Florida, Gainesville, FL Bosons: Spin-waves and BEC in thin-film ferromagnets spin-wave theory interactions and BEC Fermions: Spin fluctuation pairing and symmetry of order

More information

We can then linearize the Heisenberg equation for in the small quantity obtaining a set of linear coupled equations for and :

We can then linearize the Heisenberg equation for in the small quantity obtaining a set of linear coupled equations for and : Wednesday, April 23, 2014 9:37 PM Excitations in a Bose condensate So far: basic understanding of the ground state wavefunction for a Bose-Einstein condensate; We need to know: elementary excitations in

More information

Interaction between atoms

Interaction between atoms Interaction between atoms MICHA SCHILLING HAUPTSEMINAR: PHYSIK DER KALTEN GASE INSTITUT FÜR THEORETISCHE PHYSIK III UNIVERSITÄT STUTTGART 23.04.2013 Outline 2 Scattering theory slow particles / s-wave

More information

Ground State Projector QMC in the valence-bond basis

Ground State Projector QMC in the valence-bond basis Quantum Monte Carlo Methods at Work for Novel Phases of Matter Trieste, Italy, Jan 23 - Feb 3, 2012 Ground State Projector QMC in the valence-bond basis Anders. Sandvik, Boston University Outline: The

More information

The Quantum Theory of Magnetism

The Quantum Theory of Magnetism The Quantum Theory of Magnetism Norberto Mains McGill University, Canada I: 0 World Scientific Singapore NewJersey London Hong Kong Contents 1 Paramagnetism 1.1 Introduction 1.2 Quantum mechanics of atoms

More information

Phase Transitions in Condensed Matter Spontaneous Symmetry Breaking and Universality. Hans-Henning Klauss. Institut für Festkörperphysik TU Dresden

Phase Transitions in Condensed Matter Spontaneous Symmetry Breaking and Universality. Hans-Henning Klauss. Institut für Festkörperphysik TU Dresden Phase Transitions in Condensed Matter Spontaneous Symmetry Breaking and Universality Hans-Henning Klauss Institut für Festkörperphysik TU Dresden 1 References [1] Stephen Blundell, Magnetism in Condensed

More information

Problem Set No. 3: Canonical Quantization Due Date: Wednesday October 19, 2018, 5:00 pm. 1 Spin waves in a quantum Heisenberg antiferromagnet

Problem Set No. 3: Canonical Quantization Due Date: Wednesday October 19, 2018, 5:00 pm. 1 Spin waves in a quantum Heisenberg antiferromagnet Physics 58, Fall Semester 018 Professor Eduardo Fradkin Problem Set No. 3: Canonical Quantization Due Date: Wednesday October 19, 018, 5:00 pm 1 Spin waves in a quantum Heisenberg antiferromagnet In this

More information

FRG approach to interacting fermions with partial bosonization: from weak to strong coupling

FRG approach to interacting fermions with partial bosonization: from weak to strong coupling FRG approach to interacting fermions with partial bosonization: from weak to strong coupling Talk at conference ERG08, Heidelberg, June 30, 2008 Peter Kopietz, Universität Frankfurt collaborators: Lorenz

More information

Heisenberg-Kitaev physics in magnetic fields

Heisenberg-Kitaev physics in magnetic fields Heisenberg-Kitaev physics in magnetic fields Lukas Janssen & Eric Andrade, Matthias Vojta L.J., E. Andrade, and M. Vojta, Phys. Rev. Lett. 117, 277202 (2016) L.J., E. Andrade, and M. Vojta, Phys. Rev.

More information

The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I)

The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I) The XY model, the Bose Einstein Condensation and Superfluidity in 2d (I) B.V. COSTA UFMG BRAZIL LABORATORY FOR SIMULATION IN PHYSICS A Guide to Monte Carlo Simulations in Statistical Physics by Landau

More information

Spontaneous symmetry breaking in fermion systems with functional RG

Spontaneous symmetry breaking in fermion systems with functional RG Spontaneous symmetry breaking in fermion systems with functional RG Andreas Eberlein and Walter Metzner MPI for Solid State Research, Stuttgart Lefkada, September 24 A. Eberlein and W. Metzner Spontaneous

More information

Quantum Many Body Theory

Quantum Many Body Theory Quantum Many Body Theory Victor Gurarie Week 4 4 Applications of the creation and annihilation operators 4.1 A tight binding model Consider bosonic particles which hops around on the lattice, for simplicity,

More information

The Mermin-Wagner Theorem

The Mermin-Wagner Theorem June 24, 2010 Conclusion In one and two dimensions, continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions. Contents 1 How symmetry

More information

(Quasi-) Nambu-Goldstone Fermion in Hot QCD Plasma and Bose-Fermi Cold Atom System

(Quasi-) Nambu-Goldstone Fermion in Hot QCD Plasma and Bose-Fermi Cold Atom System (Quasi-) Nambu-Goldstone Fermion in Hot QCD Plasma and Bose-Fermi Cold Atom System Daisuke Satow (RIKEN/BNL) Collaborators: Jean-Paul Blaizot (Saclay CEA, France) Yoshimasa Hidaka (RIKEN, Japan) Supersymmetry

More information

Hole dynamics in frustrated antiferromagnets: Coexistence of many-body and free-like excitations

Hole dynamics in frustrated antiferromagnets: Coexistence of many-body and free-like excitations Hole dynamics in frustrated antiferromagnets: Coexistence of many-body and free-like excitations Collaborators: Luis O. Manuel Instituto de Física Rosario Rosario, Argentina Adolfo E. Trumper (Rosario)

More information

Linear spin wave theory

Linear spin wave theory Linear spin wave theory Sándor Tóth Paul Scherrer Institut August 17, 2015 Sándor Tóth (Paul Scherrer Institut) Linear spin wave theory August 17, 2015 1 / 48 Motivation Presentation Outline 1 Motivation

More information

Part 1. March 5, 2014 Quantum Hadron Physics Laboratory, RIKEN, Wako, Japan 2

Part 1. March 5, 2014 Quantum Hadron Physics Laboratory, RIKEN, Wako, Japan 2 MAR 5, 2014 Part 1 March 5, 2014 Quantum Hadron Physics Laboratory, RIKEN, Wako, Japan 2 ! Examples of relativistic matter Electrons, protons, quarks inside compact stars (white dwarfs, neutron, hybrid

More information

Kitaev honeycomb lattice model: from A to B and beyond

Kitaev 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 information

Winter School for Quantum Magnetism EPFL and MPI Stuttgart Magnetism in Strongly Correlated Systems Vladimir Hinkov

Winter School for Quantum Magnetism EPFL and MPI Stuttgart Magnetism in Strongly Correlated Systems Vladimir Hinkov Winter School for Quantum Magnetism EPFL and MPI Stuttgart Magnetism in Strongly Correlated Systems Vladimir Hinkov 1. Introduction Excitations and broken symmetry 2. Spin waves in the Heisenberg model

More information

Spinor Bose gases lecture outline

Spinor Bose gases lecture outline Spinor Bose gases lecture outline 1. Basic properties 2. Magnetic order of spinor Bose-Einstein condensates 3. Imaging spin textures 4. Spin-mixing dynamics 5. Magnetic excitations We re here Coupling

More information

Low dimensional interacting bosons

Low dimensional interacting bosons Low dimensional interacting bosons Serena Cenatiempo PhD defence Supervisors: E. Marinari and A. Giuliani Physics Department Sapienza, Università di Roma February 7, 2013 It was only in 1995 Anderson et

More information

Luigi Paolasini

Luigi Paolasini Luigi Paolasini paolasini@esrf.fr LECTURE 7: Magnetic excitations - Phase transitions and the Landau mean-field theory. - Heisenberg and Ising models. - Magnetic excitations. External parameter, as for

More information

Unusual ordered phases of magnetized frustrated antiferromagnets

Unusual ordered phases of magnetized frustrated antiferromagnets Unusual ordered phases of magnetized frustrated antiferromagnets Credit: Francis Pratt / ISIS / STFC Oleg Starykh University of Utah Leon Balents and Andrey Chubukov Novel states in correlated condensed

More information

1 The Heisenberg model

1 The Heisenberg model 1 The Heisenberg model 1.1 Definition of the model The model we will focus on is called the Heisenberg model. It has the following Hamiltonian: H = 1 J ij S i S j. (1) 2 i,j i j Here i and j refer to sites

More information

Quantum criticality of Fermi surfaces

Quantum criticality of Fermi surfaces Quantum criticality of Fermi surfaces Subir Sachdev Physics 268br, Spring 2018 HARVARD Quantum criticality of Ising-nematic ordering in a metal y Occupied states x Empty states A metal with a Fermi surface

More information

Quantum spin systems - models and computational methods

Quantum 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 information

Spinons and triplons in spatially anisotropic triangular antiferromagnet

Spinons and triplons in spatially anisotropic triangular antiferromagnet Spinons and triplons in spatially anisotropic triangular antiferromagnet Oleg Starykh, University of Utah Leon Balents, UC Santa Barbara Masanori Kohno, NIMS, Tsukuba PRL 98, 077205 (2007); Nature Physics

More information

BCS-BEC Crossover. Hauptseminar: Physik der kalten Gase Robin Wanke

BCS-BEC Crossover. Hauptseminar: Physik der kalten Gase Robin Wanke BCS-BEC Crossover Hauptseminar: Physik der kalten Gase Robin Wanke Outline Motivation Cold fermions BCS-Theory Gap equation Feshbach resonance Pairing BEC of molecules BCS-BEC-crossover Conclusion 2 Motivation

More information

Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain

Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain PHYSICAL REVIEW B VOLUME 60, UMBER 1 JULY 1999-II Schwinger-boson mean-field theory of the Heisenberg ferrimagnetic spin chain Congjun Wu Department of Physics, Peking University, Beijing 100871, China

More information

II.D Scattering and Fluctuations

II.D Scattering and Fluctuations II.D Scattering and Fluctuations In addition to bulk thermodynamic experiments, scattering measurements can be used to probe microscopic fluctuations at length scales of the order of the probe wavelength

More information

The Higgs particle in condensed matter

The Higgs particle in condensed matter The Higgs particle in condensed matter Assa Auerbach, Technion N. H. Lindner and A. A, Phys. Rev. B 81, 054512 (2010) D. Podolsky, A. A, and D. P. Arovas, Phys. Rev. B 84, 174522 (2011)S. Gazit, D. Podolsky,

More information

arxiv:cond-mat/ v1 2 Mar 1997

arxiv:cond-mat/ v1 2 Mar 1997 1/N Expansion for Critical Exponents of Magnetic Phase Transitions in CP N 1 Model at 2 < d < 4 V.Yu.Irkhin, A.A.Katanin and M.I.Katsnelson Institute of Metal Physics, 620219 Ekaterinburg, Russia Critical

More information

Green's Function in. Condensed Matter Physics. Wang Huaiyu. Alpha Science International Ltd. SCIENCE PRESS 2 Beijing \S7 Oxford, U.K.

Green's Function in. Condensed Matter Physics. Wang Huaiyu. Alpha Science International Ltd. SCIENCE PRESS 2 Beijing \S7 Oxford, U.K. Green's Function in Condensed Matter Physics Wang Huaiyu SCIENCE PRESS 2 Beijing \S7 Oxford, U.K. Alpha Science International Ltd. CONTENTS Part I Green's Functions in Mathematical Physics Chapter 1 Time-Independent

More information

Spin liquids in frustrated magnets

Spin 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 information

Magnets, 1D quantum system, and quantum Phase transitions

Magnets, 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 information

Decoherence in molecular magnets: Fe 8 and Mn 12

Decoherence in molecular magnets: Fe 8 and Mn 12 Decoherence in molecular magnets: Fe 8 and Mn 12 I.S. Tupitsyn (with P.C.E. Stamp) Pacific Institute of Theoretical Physics (UBC, Vancouver) Early 7-s: Fast magnetic relaxation in rare-earth systems (Dy

More information

arxiv: v2 [cond-mat.str-el] 12 Oct 2012

arxiv: v2 [cond-mat.str-el] 12 Oct 2012 arxiv:105.0977v [cond-mat.str-el] 1 Oct 01 Longitudinal excitations in triangular lattice antiferromagnets Mohammad Merdan and Y Xian School of Physics and Astronomy, The University of Manchester, Manchester

More information

Functional renormalization for ultracold quantum gases

Functional renormalization for ultracold quantum gases Functional renormalization for ultracold quantum gases Stefan Floerchinger (Heidelberg) S. Floerchinger and C. Wetterich, Phys. Rev. A 77, 053603 (2008); S. Floerchinger and C. Wetterich, arxiv:0805.2571.

More information

Dynamic Density and Spin Responses in the BCS-BEC Crossover: Toward a Theory beyond RPA

Dynamic Density and Spin Responses in the BCS-BEC Crossover: Toward a Theory beyond RPA Dynamic Density and Spin Responses in the BCS-BEC Crossover: Toward a Theory beyond RPA Lianyi He ( 何联毅 ) Department of Physics, Tsinghua University 2016 Hangzhou Workshop on Quantum Degenerate Fermi Gases,

More information

Supersymmetry breaking and Nambu-Goldstone fermions in lattice models

Supersymmetry 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 information

in-medium pair wave functions the Cooper pair wave function the superconducting order parameter anomalous averages of the field operators

in-medium pair wave functions the Cooper pair wave function the superconducting order parameter anomalous averages of the field operators (by A. A. Shanenko) in-medium wave functions in-medium pair-wave functions and spatial pair particle correlations momentum condensation and ODLRO (off-diagonal long range order) U(1) symmetry breaking

More information

Non-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. 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 information

Bogoliubov theory of the weakly interacting Bose gas

Bogoliubov theory of the weakly interacting Bose gas Chapter 4 Bogoliubov theory of the wealy interacting Bose gas In the presence of BEC, the ideal Bose gas has a constant pressure against variation of volume, so that the system features infinite compressibility.

More information

3.14. The model of Haldane on a honeycomb lattice

3.14. The model of Haldane on a honeycomb lattice 4 Phys60.n..7. Marginal case: 4 t Dirac points at k=(,). Not an insulator. No topological index...8. case IV: 4 t All the four special points has z 0. We just use u I for the whole BZ. No singularity.

More information

Topological Insulator Surface States and Electrical Transport. Alexander Pearce Intro to Topological Insulators: Week 11 February 2, / 21

Topological Insulator Surface States and Electrical Transport. Alexander Pearce Intro to Topological Insulators: Week 11 February 2, / 21 Topological Insulator Surface States and Electrical Transport Alexander Pearce Intro to Topological Insulators: Week 11 February 2, 2017 1 / 21 This notes are predominately based on: J.K. Asbóth, L. Oroszlány

More information

Proximity-induced magnetization dynamics, interaction effects, and phase transitions on a topological surface

Proximity-induced magnetization dynamics, interaction effects, and phase transitions on a topological surface Proximity-induced magnetization dynamics, interaction effects, and phase transitions on a topological surface Ilya Eremin Theoretische Physik III, Ruhr-Uni Bochum Work done in collaboration with: F. Nogueira

More information

Drag force and superfluidity in the supersolid striped phase of a spin-orbit-coupled Bose gas

Drag force and superfluidity in the supersolid striped phase of a spin-orbit-coupled Bose gas / 6 Drag force and superfluidity in the supersolid striped phase of a spin-orbit-coupled Bose gas Giovanni Italo Martone with G. V. Shlyapnikov Worhshop on Exploring Nuclear Physics with Ultracold Atoms

More information

Spinon magnetic resonance. Oleg Starykh, University of Utah

Spinon magnetic resonance. Oleg Starykh, University of Utah Spinon magnetic resonance Oleg Starykh, University of Utah May 17-19, 2018 Examples of current literature 200 cm -1 = 6 THz Spinons? 4 mev = 1 THz The big question(s) What is quantum spin liquid? No broken

More information

Spin-wave dispersion in half-doped La3/2Sr1/2NiO4

Spin-wave dispersion in half-doped La3/2Sr1/2NiO4 Physics Physics Research Publications Purdue University Year 2007 Spin-wave dispersion in half-doped La3/2Sr1/2NiO4 D. X. Yao E. W. Carlson This paper is posted at Purdue e-pubs. http://docs.lib.purdue.edu/physics

More information

ICAP Summer School, Paris, Three lectures on quantum gases. Wolfgang Ketterle, MIT

ICAP Summer School, Paris, Three lectures on quantum gases. Wolfgang Ketterle, MIT ICAP Summer School, Paris, 2012 Three lectures on quantum gases Wolfgang Ketterle, MIT Cold fermions Reference for most of this talk: W. Ketterle and M. W. Zwierlein: Making, probing and understanding

More information

STUDY OF THE EXCITED STATES OF THE QUANTUM ANTIFERROMAGNETS

STUDY OF THE EXCITED STATES OF THE QUANTUM ANTIFERROMAGNETS STUDY OF THE EXCITED STATES OF THE QUANTUM ANTIFERROMAGNETS A THESIS SUBMITTED TO THE UNIVERSITY OF MANCHESTER FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF ENGINEERING AND PHYSICAL SCIENCES

More information

Transport theory and low energy properties of colour superconductors

Transport theory and low energy properties of colour superconductors 1 Transport theory and low energy properties of colour superconductors Daniel F. Litim Theory Group, CERN, CH 1211 Geneva 23, Switzerland. CERN-TH-2001-315 The one-loop polarisation tensor and the propagation

More information

Physics 127b: Statistical Mechanics. Landau Theory of Second Order Phase Transitions. Order Parameter

Physics 127b: Statistical Mechanics. Landau Theory of Second Order Phase Transitions. Order Parameter Physics 127b: Statistical Mechanics Landau Theory of Second Order Phase Transitions Order Parameter Second order phase transitions occur when a new state of reduced symmetry develops continuously from

More information

Multiple spin exchange model on the triangular lattice

Multiple spin exchange model on the triangular lattice Multiple spin exchange model on the triangular lattice Philippe Sindzingre, Condensed matter theory laboratory Univ. Pierre & Marie Curie Kenn Kubo Aoyama Gakuin Univ Tsutomu Momoi RIKEN T. Momoi, P. Sindzingre,

More information

Spin liquids on ladders and in 2d

Spin 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 information

Collective Effects. Equilibrium and Nonequilibrium Physics

Collective Effects. Equilibrium and Nonequilibrium Physics Collective Effects in Equilibrium and Nonequilibrium Physics: Lecture 3, 3 March 2006 Collective Effects in Equilibrium and Nonequilibrium Physics Website: http://cncs.bnu.edu.cn/mccross/course/ Caltech

More information

Diagrammatic Green s Functions Approach to the Bose-Hubbard Model

Diagrammatic Green s Functions Approach to the Bose-Hubbard Model Diagrammatic Green s Functions Approach to the Bose-Hubbard Model Matthias Ohliger Institut für Theoretische Physik Freie Universität Berlin 22nd of January 2008 Content OVERVIEW CONSIDERED SYSTEM BASIC

More information

arxiv:cond-mat/ v1 [cond-mat.str-el] 15 Jul 2005

arxiv:cond-mat/ v1 [cond-mat.str-el] 15 Jul 2005 Correlation functions of one-dimensional Bose-Fermi mixtures Holger Frahm and Guillaume Palacios Institut für Theoretische Physik, Universität Hannover, Appelstr. 2, 30167 Hannover, Germany (Dated: July

More information

Longitudinal spin fluctuations in the antiferromagnet MnF 2 studied by polarized neutron scattering

Longitudinal spin fluctuations in the antiferromagnet MnF 2 studied by polarized neutron scattering EUROPHYSICS LETTERS 1 November 22 Europhys. Lett., 6 (3), pp. 446 452 (22) Longitudinal spin fluctuations in the antiferromagnet MnF 2 studied by polarized neutron scattering W. Schweika 1,S.V.Maleyev

More information

Superfluidity and spin superfluidity (in spinor Bose gases and magnetic insulators)

Superfluidity and spin superfluidity (in spinor Bose gases and magnetic insulators) Superfluidity and spin superfluidity (in spinor Bose gases and magnetic insulators) Rembert Duine Institute for Theoretical Physics, Utrecht University Department of Applied Physics, Eindhoven University

More information

Cooperative Phenomena

Cooperative Phenomena Cooperative Phenomena Frankfurt am Main Kaiserslautern Mainz B1, B2, B4, B6, B13N A7, A9, A12 A10, B5, B8 Materials Design - Synthesis & Modelling A3, A8, B1, B2, B4, B6, B9, B11, B13N A5, A7, A9, A12,

More information

Solution of the Anderson impurity model via the functional renormalization group

Solution of the Anderson impurity model via the functional renormalization group Solution of the Anderson impurity model via the functional renormalization group Simon Streib, Aldo Isidori, and Peter Kopietz Institut für Theoretische Physik, Goethe-Universität Frankfurt Meeting DFG-Forschergruppe

More information

1 Equal-time and Time-ordered Green Functions

1 Equal-time and Time-ordered Green Functions 1 Equal-time and Time-ordered Green Functions Predictions for observables in quantum field theories are made by computing expectation values of products of field operators, which are called Green functions

More information

5 Topological insulator with time-reversal symmetry

5 Topological insulator with time-reversal symmetry Phys62.nb 63 5 Topological insulator with time-reversal symmetry It is impossible to have quantum Hall effect without breaking the time-reversal symmetry. xy xy. If we want xy to be invariant under, xy

More information

The bosonic Kondo effect:

The bosonic Kondo effect: The bosonic Kondo effect: probing spin liquids and multicomponent cold gases Serge Florens Institut für Theorie der Kondensierten Materie (Karlsruhe) with: Lars Fritz, ITKM (Karlsruhe) Matthias Vojta,

More information

The ultrametric tree of states and computation of correlation functions in spin glasses. Andrea Lucarelli

The ultrametric tree of states and computation of correlation functions in spin glasses. Andrea Lucarelli Università degli studi di Roma La Sapienza Facoltà di Scienze Matematiche, Fisiche e Naturali Scuola di Dottorato Vito Volterra Prof. Giorgio Parisi The ultrametric tree of states and computation of correlation

More information

Exact diagonalization methods

Exact diagonalization methods Summer School on Computational Statistical Physics August 4-11, 2010, NCCU, Taipei, Taiwan Exact diagonalization methods Anders W. Sandvik, Boston University Representation of states in the computer bit

More information

Excitonic Condensation in Systems of Strongly Correlated Electrons. Jan Kuneš and Pavel Augustinský DFG FOR1346

Excitonic Condensation in Systems of Strongly Correlated Electrons. Jan Kuneš and Pavel Augustinský DFG FOR1346 Excitonic Condensation in Systems of Strongly Correlated Electrons Jan Kuneš and Pavel Augustinský DFG FOR1346 Motivation - unconventional long-range order incommensurate spin spirals complex order parameters

More information

2D Bose and Non-Fermi Liquid Metals

2D 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 information

Phase transitions and critical phenomena

Phase transitions and critical phenomena Phase transitions and critical phenomena Classification of phase transitions. Discontinous (st order) transitions Summary week -5 st derivatives of thermodynamic potentials jump discontinously, e.g. (

More information

Talk online at

Talk online at Talk online at http://sachdev.physics.harvard.edu Outline 1. CFT3s in condensed matter physics Superfluid-insulator and Neel-valence bond solid transitions 2. Quantum-critical transport Collisionless-t0-hydrodynamic

More information

Quantum dynamics in many body systems

Quantum dynamics in many body systems Quantum dynamics in many body systems Eugene Demler Harvard University Collaborators: David Benjamin (Harvard), Israel Klich (U. Virginia), D. Abanin (Perimeter), K. Agarwal (Harvard), E. Dalla Torre (Harvard)

More information

Topological sector of two dimensional φ 4 theory in Discrete Light Cone Quantization p. 1/3

Topological sector of two dimensional φ 4 theory in Discrete Light Cone Quantization p. 1/3 Topological sector of two dimensional φ 4 theory in Discrete Light Cone Quantization p. 1/3 Topological sector of two dimensional φ 4 theory in Discrete Light Cone Quantization A. H (Theory Division, SINP,

More information

Global phase diagrams of two-dimensional quantum antiferromagnets. Subir Sachdev Harvard University

Global 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 information

Fermionic condensation in ultracold atoms, nuclear matter and neutron stars

Fermionic condensation in ultracold atoms, nuclear matter and neutron stars Fermionic condensation in ultracold atoms, nuclear matter and neutron stars Luca Salasnich Dipartimento di Fisica e Astronomia Galileo Galilei, Università di Padova, Italy Prague, July 16, 2013 Collaboration

More information

Reference for most of this talk:

Reference for most of this talk: Cold fermions Reference for most of this talk: W. Ketterle and M. W. Zwierlein: Making, probing and understanding ultracold Fermi gases. in Ultracold Fermi Gases, Proceedings of the International School

More information

Quasi-1d Antiferromagnets

Quasi-1d Antiferromagnets Quasi-1d Antiferromagnets Leon Balents, UCSB Masanori Kohno, NIMS, Tsukuba Oleg Starykh, U. Utah Quantum Fluids, Nordita 2007 Outline Motivation: Quantum magnetism and the search for spin liquids Neutron

More information

ROTONS AND STRIPES IN SPIN-ORBIT COUPLED BECs

ROTONS AND STRIPES IN SPIN-ORBIT COUPLED BECs INT Seattle 5 March 5 ROTONS AND STRIPES IN SPIN-ORBIT COUPLED BECs Yun Li, Giovanni Martone, Lev Pitaevskii and Sandro Stringari University of Trento CNR-INO Now in Swinburne Now in Bari Stimulating discussions

More information

Kolloquium Universität Innsbruck October 13, The renormalization group: from the foundations to modern applications

Kolloquium Universität Innsbruck October 13, The renormalization group: from the foundations to modern applications Kolloquium Universität Innsbruck October 13, 2009 The renormalization group: from the foundations to modern applications Peter Kopietz, Universität Frankfurt 1.) Historical introduction: what is the RG?

More information

Quark Structure of the Pion

Quark Structure of the Pion Quark Structure of the Pion Hyun-Chul Kim RCNP, Osaka University & Department of Physics, Inha University Collaborators: H.D. Son, S.i. Nam Progress of J-PARC Hadron Physics, Nov. 30-Dec. 01, 2014 Interpretation

More information

Thermal Hall effect of magnons

Thermal Hall effect of magnons Max Planck-UBC-UTokyo School@Hongo (2018/2/18) Thermal Hall effect of magnons Hosho Katsura (Dept. Phys., UTokyo) Related papers: H.K., Nagaosa, Lee, Phys. Rev. Lett. 104, 066403 (2010). Onose et al.,

More information

Renormalization Group: non perturbative aspects and applications in statistical and solid state physics.

Renormalization Group: non perturbative aspects and applications in statistical and solid state physics. Renormalization Group: non perturbative aspects and applications in statistical and solid state physics. Bertrand Delamotte Saclay, march 3, 2009 Introduction Field theory: - infinitely many degrees of

More information

Quasi-1d Frustrated Antiferromagnets. Leon Balents, UCSB Masanori Kohno, NIMS, Tsukuba Oleg Starykh, U. Utah

Quasi-1d Frustrated Antiferromagnets. Leon Balents, UCSB Masanori Kohno, NIMS, Tsukuba Oleg Starykh, U. Utah Quasi-1d Frustrated Antiferromagnets Leon Balents, UCSB Masanori Kohno, NIMS, Tsukuba Oleg Starykh, U. Utah Outline Frustration in quasi-1d systems Excitations: magnons versus spinons Neutron scattering

More information

A New Electronic Orbital Order Identified in Parent Compound of Fe-Based High-Temperature Superconductors

A New Electronic Orbital Order Identified in Parent Compound of Fe-Based High-Temperature Superconductors A New Electronic Orbital Order Identified in Parent Compound of Fe-Based High-Temperature Superconductors Cooperative Research Team on Predictive Capability for Strongly Correlated Systems Summary: The

More information

Critical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets. In collaboration with: Olexei Motrunich & Jason Alicea

Critical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets. In collaboration with: Olexei Motrunich & Jason Alicea Critical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets In collaboration with: Olexei Motrunich & Jason Alicea I. Background Outline Avoiding conventional symmetry-breaking in s=1/2 AF Topological

More information

Ideas on non-fermi liquid metals and quantum criticality. T. Senthil (MIT).

Ideas on non-fermi liquid metals and quantum criticality. T. Senthil (MIT). Ideas on non-fermi liquid metals and quantum criticality T. Senthil (MIT). Plan Lecture 1: General discussion of heavy fermi liquids and their magnetism Review of some experiments Concrete `Kondo breakdown

More information

PION DECAY CONSTANT AT FINITE TEMPERATURE IN THE NONLINEAR SIGMA MODEL

PION DECAY CONSTANT AT FINITE TEMPERATURE IN THE NONLINEAR SIGMA MODEL NUC-MINN-96/3-T February 1996 arxiv:hep-ph/9602400v1 26 Feb 1996 PION DECAY CONSTANT AT FINITE TEMPERATURE IN THE NONLINEAR SIGMA MODEL Sangyong Jeon and Joseph Kapusta School of Physics and Astronomy

More information

Magnetism in ultracold gases

Magnetism in ultracold gases Magnetism in ultracold gases Austen Lamacraft Theoretical condensed matter and atomic physics April 10th, 2009 faculty.virginia.edu/austen/ Outline Magnetism in condensed matter Ultracold atomic physics

More information

Problem set for the course Skálázás és renormálás a statisztikus fizikában, 2014

Problem set for the course Skálázás és renormálás a statisztikus fizikában, 2014 1 Problem set for the course Skálázás és renormálás a statisztikus fizikában, 014 Rules: You can choose at wish from problems having the same main number (i.e. from a given section), but you can collect

More information

Phase transitions in Hubbard Model

Phase transitions in Hubbard Model Phase transitions in Hubbard Model Anti-ferromagnetic and superconducting order in the Hubbard model A functional renormalization group study T.Baier, E.Bick, C.Krahl, J.Mueller, S.Friederich Phase diagram

More information

Symmetry protected topological phases in quantum spin systems

Symmetry protected topological phases in quantum spin systems 10sor network workshop @Kashiwanoha Future Center May 14 (Thu.), 2015 Symmetry protected topological phases in quantum spin systems NIMS U. Tokyo Shintaro Takayoshi Collaboration with A. Tanaka (NIMS)

More information

EXPLODING BOSE-EINSTEIN CONDENSATES AND COLLAPSING NEUTRON STARS DRIVEN BY CRITICAL MAGNETIC FIELDS

EXPLODING BOSE-EINSTEIN CONDENSATES AND COLLAPSING NEUTRON STARS DRIVEN BY CRITICAL MAGNETIC FIELDS EXPLODING BOSE-EINSTEIN CONDENSATES AND COLLAPSING NEUTRON STARS DRIVEN BY CRITICAL MAGNETIC FIELDS H. PÉREZ ROJAS, A. PÉREZ MARTíNEZ Instituto de Cibernética, Matemática y Física, 10400 La Habana, Cuba

More information

Ultracold Fermi and Bose Gases and Spinless Bose Charged Sound Particles

Ultracold Fermi and Bose Gases and Spinless Bose Charged Sound Particles October, 011 PROGRESS IN PHYSICS olume 4 Ultracold Fermi Bose Gases Spinless Bose Charged Sound Particles ahan N. Minasyan alentin N. Samoylov Scientific Center of Applied Research, JINR, Dubna, 141980,

More information