Wilsonian and large N theories of quantum critical metals. Srinivas Raghu (Stanford)
|
|
- Dale Malone
- 5 years ago
- Views:
Transcription
1 Wilsonian and large N theories of quantum critical metals Srinivas Raghu (Stanford)
2 Collaborators and References R. Mahajan, D. Ramirez, S. Kachru, and SR, PRB 88, (2013). A. Liam Fitzpatrick, S. Kachru, J. Kaplan, and SR, PRB 88, (2013). A. Liam Fitzpatrick, S. Kachru, J. Kaplan, and SR, PRB (2014). A. Liam Fitzpatrick, S. Kachru, J. Kaplan, and SR, to appear. With Liam Fitzpatrick, Jared Kaplan, Shamit Kachru
3 Breakdown of fermion quasiparticles A recurring theme: Fermi liquid theory breaks down at a quantum phase transition. NFL emanates from a critical point at T=0. NFL can give way to higher Tc superconductivity. QCPs in metals: wide-open problem especially in d=2+1. NFL
4 BaFe2(As1-xPx)2 Example: Iron pnictides EVOLUTION FROM NON-FERMI- TO FERMI-LIQUID ρ xx ( µω cm) R H (10-3 cm 3 /C) x= T (K) ~ T 1.0 ~ T 1.2 ~ T 1.7 ~ T 1.9 = x ~ T T (K) x =0.33 x =0.41 x =0.56 x =0.64 (a) ρ xx (H)/ρ xx K 50 K 60 K 80 K 100 K ρ xx (H)/ρ xx tan (b) 2 Θ 0 H (µ 0 H/ρ xx ) 2 (T 2 /(µω cm) 2 ) FIG. 3. Color online a Normal-state xx T for x=0.33, 0.41, 0.56, 0.64, and 0.71 at low temperatures can be fitted by the power Maximum superconducting Tc law Eq. 1. The inset shows T dependence of R H T for x below the NFL. =0.33. Solid line is a fit to the data by R H T =C 1 /T+C 2 with C 1 =0.048 Kcm 3 /C and C 2 = cm 3 /C. b Magnetoresistanceout xx of H / a xx plotted as a function of 0 H/ xx 2 for x=0.33. Superconductivity forms non-fermi liquid. The inset shows xx H / xx plotted as a function tan 2 H. FIG. 5. Evidence for the QCP in the superconducting dome in Talk by Prof. Shibauchi in the symposium. BaFe 2 (As 1 x P x ) 2. (a) Temperature dependence of in-plane resistivity ρ xx for [50]. [PNAS The2009, red lines PRB 2010] are the fit of normal-state ρ xx (T )topower-lawdependenceρ 0 + AT α FIG. 5. Evidence for the QCP in the superconducting dome in t r o g n a h K d w s t c w c N
5 Fermi liquid Concrete model system Via Pomeranchuk Via meltingbreaking of point group symmetry. Ising nematic transition: instability stripes 2 possible ground states spin up spin down Nematic phases Figure 1 Nematic phases Via Pomeranchuk instability Fermi liquid Pomeranchuk instability Fermi liquid Fermi liquids: Analogy with classical liquid crystals Two different mechanisms for producing a nematic phase with point particles: The gentle melting of a Via Pomeranchuk t Alternatively, a nematic Fermi fluid can arise through the distortion of the Fermi surface of a metal via stripe phase can restore long-range translational symmetry while preserving orientational order (8). instability a Pomeranchuk instability (27, 28). (After, in part, Reference 8.) order Smectic or stripe phase c e Smectic or stripe phase parameter: t+ Via melting stripes thermal melting of a stripe state to form a nematic fluid is readily understood theoretically and, indeed, the resulting description is similar to the theory of the nearly Nematic phases (9, 18, 29 31)Nematic Isotropic smectic nematic fluid that has been developed in the context of complex classical fluids (2, 32). Within this perspective, the nematic state arises from the proliferation of dislocations, the topological defects of the stripe state. This can take place either via a thermal The nematic state preserves lattice translation symmetry. phase transition (as in the standard classical case) or as a quantum phase transition. Whereas the thermal phase transition is well understood (2, 32), the theory of the quantum smectic-nematic phase transition by a dislocation proliferation mechanism is largely an
6 Effective theory: Fermion-boson problem Starting UV action: S = S + S + S S S S Landau Fermi liquid Landau-Ginzburg-Wilson theory for order parameter. Fermion-boson Yukawa coupling Obtaining such an action: Start with electrons strongly interacting ( Hubbard model ). Integrate out high energy modes from lattice scale down to a new UV cutoff << E F. = Scale below which we can linearize the fermion Kinetic energy.
7 Effective theory: Fermion-boson problem Starting UV action (in imaginary time): een bosons and fermions: S = d d d x L = S + S + S L = [ + µ (i )] + 2 L = m 2 2 +( ) 2 + c 2 + 4! 4 d d+1 kd d+1 q S, = (2 ) g(k, q) (k) (k + q) (q), 2(d+1) Fermions bosons Yukawa coupling Ising nematic theory: g(k, q) =g (cos k x cos k y ). g=0: decoupled limit (Fermi liquid + ordinary critical point). non-zero g: complex tug-of-war between bosons and fermions.
8 Tug-of-war between bosons and fermions Non-zero g: Bosons can decay into particle-hole continuum -> overdamped bosons. a ab ab + b Non-zero g: Quasiparticle scattering enhanced due to bosons. ab a b a + q.p. Scattering rate can exceed its energy. Fermion propagators: poles become branch cuts. Result: breakdown of Landau quasiparticle. How to proceed???
9 Large N limits
10 Large N limits Essence of the problem: dissipative coupling between bosons and fermions. Large N limits: particles with many (N) flavors act as a dissipative bath while remaining degrees of freedom become overdamped. e.g. Large number of fermion flavors (Nf). Boson can decay in many channels -> Overdamped bosons (NFL is subdominant). Mainstream (Hertz) theory captures the IR behavior in this regime. e.g. Large number of boson flavors (Nb). Fermion can decay in many channels -> NFL is strongest effect (boson damping is subdominant).
11 Large N limits Large NF: O(1/N F ): Large NB: O(1/N B ):
12 Implementation of large N limits! i! i =1 N F i, j =1 N B! j i g! g i j j i (repeated indices summed). I will consider the case: N F =1,N B!1.
13 Large NB action L = i [@ + µ (ir)] i + i NB L =tr m (@ ) 2 + c 2 r ~ i j j (1) + tr( 4 )+ 8N B L, = g p NB i j j i (2) 8N 2 B (tr( 2 )) 2 i, j =1 N B Impose an SO(NB 2 ) symmetry: (1) =0 This symmetry is softly broken: i.e., only at O(1/N 2 B).
14 N B!1: = Large NB solution Properties of the solution: G(k,!) = 1) Fermi velocity vanishes at infinite NB. 2) Green function has branch cut spectrum. 3) Damping of order parameter is a 1/NB effect. =3 d 1! 1 /2 f! k ; N B! f k ; N B!1 =1 The solution matches on to perturbation theory in the UV. The theory can smoothly be extended to d=2. The theory describes infinitely heavy, incoherent fermionic quasiparticles. We are currently investigating the strong CDW and superconducting instabilities of this system.
15 Scaling landscape N B Our theory?? Real materials Hertz N F Moral of the story: there may be several distinct asymptotic limits with different scaling behaviors, dynamic crossovers in this problem.
16 Wilsonian RG analysis
17 Scaling near the upper-critical dimension UV theory: decoupled Fermi liquid+ nearly free bosons (g=0). (a) q y (b) empty states q y Scaling must contend with vastly different kinematics of bosons and fermions. (c) q x q k k + q filled states empty states filled states q x Fermions: low energy = Fermi surface. -> anisotropic scaling. Bosons: low energy = point in k-space. -> isotropic scaling. }Scale to preserve kinetic terms. [g] = 1 (3 d) 2 Result: d=3 is the upper critical dimension.
18 Renormalization group analysis Integrate out modes with energy Integrate out modes with momenta e t <E< k e t <k< k k / = UV cutoff: scale below which fermion dispersion can be linearized (with a well-defined Fermi velocity). Following Wilson, we will integrate out only highenergy modes to obtain RG flows. This is a radical departure from the standard approach to this problem. K. G. Wilson
19 Renormalization group analysis RG flows at one-loop: =3 d 4 term : d dt = a 2 a>0 g term : Fermi velocity: dg dt = 2 g dv bg3 b>0 dt = cg2 S(v) S(v) sgn(v) Naive fixed point: = O( ) g = O( p ) v =0
20 Properties of the naive fixed point v/c: vanishes before the system reaches the fixed point! This feature shuts down Landau damping. Fermion 2-pt function takes the form: G(!,k)= 1! 1 2 f! k? f(x) = scaling function Consistent with the large NB solution. Is this too much of a good thing?? Infinitely heavy, incoherent fermions + non-mean-field critical exponents!
21 Introducing leading irrelevant couplings (k) µ = v` + w`2 + w ~ band curvature RG flow equations dv dt = cg2 S(v) S(v) sgn(v) dw dt = w w cannot be neglected below an emergent energy scale: µ e v 0/g 2 0, O(1) w is dangerously irrelevant We don t know what happens below this scale (Lifshitz transition?)
22 Current and future work There are log-squared divergences in the Cooper channel in the vicinity of the quantum critical point. This reflects a much stronger superconducting tendency! Break inversion and time-reversal symmetry: these effects are gone. More detailed, systematic treatment is in progress. Related work: Metlitski et al Goal: to demonstrate enhanced superconductivity out of a non-fermi liquid.
23 Summary and outlook We studied a metal near a nematic quantum critical point and found non-fermi liquid phenomena via 1) large N and 2)RG methods. Both methods produce consistent results. The fixed point corresponds to an infinitely heavy incoherent soup of fermions + order parameter fluctuations. This fixed point is unstable, but it governs scaling laws over a broad range of energy/temperature scales. We are currently investigating experimental properties (eg. heat capacity) and superconducting/cdw instabilities in this regime.
24 Appendix
25 Scaling analysis Fermions: only momentum component normal to Fermi surface scale with energy:! 0 = e t!, k 0 F = k F, `0 = e t` ~ k ~` Fermi surface BCS coupling: 0 = ~ kf Bosons: all components of momentum scale with energy: ~q! 0 = e t!, k 0 = e t k quartic term: 0 = e (3 d)t
26 Scaling analysis Boson-fermion coupling: For small momentum transfer, the coupling is marginal in d=3. ~q Fermi surface ~ k ~k + ~q This coupling becomes relevant when d < 3, as is true for boson interactions: g 0 = e 3 d 2 t 0 g = e (3 d)t This results in non-trivial fixed points in d<3.
Quantum critical metals and their instabilities. Srinivas Raghu (Stanford)
Quantum critical metals and their instabilities Srinivas Raghu (Stanford) Collaborators and References R. Mahajan, D. Ramirez, S. Kachru, and SR, PRB 88, 115116 (2013). A. Liam Fitzpatrick, S. Kachru,
More information3. Quantum matter without quasiparticles
1. Review of Fermi liquid theory Topological argument for the Luttinger theorem 2. Fractionalized Fermi liquid A Fermi liquid co-existing with topological order for the pseudogap metal 3. Quantum matter
More informationQuantum 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 informationMetals without quasiparticles
Metals without quasiparticles A. Review of Fermi liquid theory B. A non-fermi liquid: the Ising-nematic quantum critical point C. Fermi surfaces and gauge fields Metals without quasiparticles A. Review
More informationA non-fermi liquid: Quantum criticality of metals near the Pomeranchuk instability
A non-fermi liquid: Quantum criticality of metals near the Pomeranchuk instability Subir Sachdev sachdev.physics.harvard.edu HARVARD y x Fermi surface with full square lattice symmetry y x Spontaneous
More informationQuantum Melting of Stripes
Quantum Melting of Stripes David Mross and T. Senthil (MIT) D. Mross, TS, PRL 2012 D. Mross, TS, PR B (to appear) Varieties of Stripes Spin, Charge Néel 2π Q c 2π Q s ``Anti-phase stripes, common in La-based
More informationEmergent Quantum Criticality
(Non-)Fermi Liquids and Emergent Quantum Criticality from gravity Hong Liu Massachusetts setts Institute te of Technology HL, John McGreevy, David Vegh, 0903.2477 Tom Faulkner, HL, JM, DV, to appear Sung-Sik
More informationIntertwined Orders in High Temperature Superconductors
Intertwined Orders in High Temperature Superconductors! Eduardo Fradkin University of Illinois at Urbana-Champaign! Talk at SCES@60 Institute for Condensed Matter Theory University of Illinois at Urbana-Champaign
More informationQuantum phase transitions of insulators, superconductors and metals in two dimensions
Quantum phase transitions of insulators, superconductors and metals in two dimensions Talk online: sachdev.physics.harvard.edu HARVARD Outline 1. Phenomenology of the cuprate superconductors (and other
More informationPhase Transitions and Renormalization:
Phase Transitions and Renormalization: Using quantum techniques to understand critical phenomena. Sean Pohorence Department of Applied Mathematics and Theoretical Physics University of Cambridge CAPS 2013
More informationLandau s Fermi Liquid Theory
Thors Hans Hansson Stockholm University Outline 1 Fermi Liquids Why, What, and How? Why Fermi liquids? What is a Fermi liquids? Fermi Liquids How? 2 Landau s Phenomenological Approach The free Fermi gas
More informationSingularites in Fermi liquids and the instability of a ferromagnetic quantum-critical point
Singularites in ermi liquids and the instability of a ferromagnetic quantum-critical point Andrey Chubukov Dmitrii Maslov lorida University of Wisconsin Catherine Pepin Jerome Rech SPhT Saclay Dima Kveshchenko
More informationIdeas 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 informationStrongly correlated Cooper pair insulators and superfluids
Strongly correlated Cooper pair insulators and superfluids Predrag Nikolić George Mason University Acknowledgments Collaborators Subir Sachdev Eun-Gook Moon Anton Burkov Arun Paramekanti Affiliations and
More informationGeneral relativity and the cuprates
General relativity and the cuprates Gary T. Horowitz and Jorge E. Santos Department of Physics, University of California, Santa Barbara, CA 93106, U.S.A. E-mail: gary@physics.ucsb.edu, jss55@physics.ucsb.edu
More informationCan superconductivity emerge out of a non Fermi liquid.
Can superconductivity emerge out of a non Fermi liquid. Andrey Chubukov University of Wisconsin Washington University, January 29, 2003 Superconductivity Kamerling Onnes, 1911 Ideal diamagnetism High Tc
More informationNematic and Magnetic orders in Fe-based Superconductors
Nematic and Magnetic orders in Fe-based Superconductors Cenke Xu Harvard University Collaborators: Markus Mueller, Yang Qi Subir Sachdev, Jiangping Hu Collaborators: Subir Sachdev Markus Mueller Yang Qi
More informationExamples of Lifshitz topological transition in interacting fermionic systems
Examples of Lifshitz topological transition in interacting fermionic systems Joseph Betouras (Loughborough U. Work in collaboration with: Sergey Slizovskiy (Loughborough, Sam Carr (Karlsruhe/Kent and Jorge
More informationFRG 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 informationFermi Liquid and BCS Phase Transition
Fermi Liquid and BCS Phase Transition Yu, Zhenhua November 2, 25 Abstract Landau fermi liquid theory is introduced as a successful theory describing the low energy properties of most fermi systems. Besides
More informationStrange metal from local quantum chaos
Strange metal from local quantum chaos John McGreevy (UCSD) hello based on work with Daniel Ben-Zion (UCSD) 2017-08-26 Compressible states of fermions at finite density The metallic states that we understand
More informationSupersymmetric Mirror Duality and Half-filled Landau level S. Kachru, M Mulligan, G Torroba and H. Wang Phys.Rev.
Supersymmetric Mirror Duality and Half-filled Landau level S. Kachru, M Mulligan, G Torroba and H. Wang Phys.Rev. B92 (2015) 235105 Huajia Wang University of Illinois Urbana Champaign Introduction/Motivation
More informationField Theories in Condensed Matter Physics. Edited by. Sumathi Rao. Harish-Chandra Research Institute Allahabad. lop
Field Theories in Condensed Matter Physics Edited by Sumathi Rao Harish-Chandra Research Institute Allahabad lop Institute of Physics Publishing Bristol and Philadelphia Contents Preface xiii Introduction
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 informationRenormalization 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 informationStability of semi-metals : (partial) classification of semi-metals
: (partial) classification of semi-metals Eun-Gook Moon Department of Physics, UCSB EQPCM 2013 at ISSP, Jun 20, 2013 Collaborators Cenke Xu, UCSB Yong Baek, Kim Univ. of Toronto Leon Balents, KITP B.J.
More informationEmergent Frontiers in Quantum Materials:
Emergent Frontiers in Quantum Materials: High Temperature superconductivity and Topological Phases Jiun-Haw Chu University of Washington The nature of the problem in Condensed Matter Physics Consider a
More informationThe Role of Charge Order in the Mechanism of High Temperature Superconductivity
The Role of Charge Order in the Mechanism of High Temperature Superconductivity Talk at the Oak Ridge National Laboratory, March 28, 2008 Eduardo Fradkin Department of Physics University of Illinois at
More informationQuantum Phase Transitions in Fermi Liquids
Quantum Phase Transitions in Fermi Liquids in d=1 and higher dimensions Mihir Khadilkar Kyungmin Lee Shivam Ghosh PHYS 7653 December 2, 2010 Outline 1 Introduction 2 d = 1: Mean field vs RG Model 3 Higher
More informationTopological order in the pseudogap metal
HARVARD Topological order in the pseudogap metal High Temperature Superconductivity Unifying Themes in Diverse Materials 2018 Aspen Winter Conference Aspen Center for Physics Subir Sachdev January 16,
More informationElectronic Liquid Crystal Phases in Strongly Correlated Systems
Electronic Liquid Crystal Phases in Strongly Correlated Systems Eduardo Fradkin University of Illinois at Urbana-Champaign Talk at the workshop Materials and the Imagination, Aspen Center of Physics, January
More information(Effective) Field Theory and Emergence in Condensed Matter
(Effective) Field Theory and Emergence in Condensed Matter T. Senthil (MIT) Effective field theory in condensed matter physics Microscopic models (e.g, Hubbard/t-J, lattice spin Hamiltonians, etc) `Low
More informationHolographic transport with random-field disorder. Andrew Lucas
Holographic transport with random-field disorder Andrew Lucas Harvard Physics Quantum Field Theory, String Theory and Condensed Matter Physics: Orthodox Academy of Crete September 1, 2014 Collaborators
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 informationVortex States in a Non-Abelian Magnetic Field
Vortex States in a Non-Abelian Magnetic Field Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University SESAPS November 10, 2016 Acknowledgments Collin Broholm IQM
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 informationarxiv: v2 [cond-mat.str-el] 2 Apr 2014
Transport near the Ising-nematic quantum critical point of metals in two dimensions Sean A. Hartnoll, 1 Raghu Mahajan, 1 Matthias Punk, 2, 3 and Subir Sachdev 4 1 Department of Physics, Stanford University,
More informationɛ(k) = h2 k 2 2m, k F = (3π 2 n) 1/3
4D-XY Quantum Criticality in Underdoped High-T c cuprates M. Franz University of British Columbia franz@physics.ubc.ca February 22, 2005 In collaboration with: A.P. Iyengar (theory) D.P. Broun, D.A. Bonn
More informationContents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9
Preface v Chapter 1 Introduction 1 1.1 Prerequisites and textbooks......................... 1 1.2 Physical phenomena and theoretical tools................. 5 1.3 The path integrals..............................
More informationQuantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals
Kerson Huang Quantum Field Theory From Operators to Path Integrals Second, Revised, and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I vh Contents Preface XIII 1 Introducing Quantum Fields
More informationThe Role of Charge Order in the Mechanism of High Temperature Superconductivity
The Role of Charge Order in the Mechanism of High Temperature Superconductivity Eduardo Fradkin Department of Physics University of Illinois at Urbana-Champaign Steven Kivelson, UCLA/Stanford Enrico Arrigoni,
More informationORBITAL SELECTIVITY AND HUND S PHYSICS IN IRON-BASED SC. Laura Fanfarillo
ORBITAL SELECTIVITY AND HUND S PHYSICS IN IRON-BASED SC Laura Fanfarillo FROM FERMI LIQUID TO NON-FERMI LIQUID Strong Correlation Bad Metal High Temperature Fermi Liquid Low Temperature Tuning parameter
More informationMOTTNESS AND STRONG COUPLING
MOTTNESS AND STRONG COUPLING ROB LEIGH UNIVERSITY OF ILLINOIS Rutgers University April 2008 based on various papers with Philip Phillips and Ting-Pong Choy PRL 99 (2007) 046404 PRB 77 (2008) 014512 PRB
More informationUniversal Post-quench Dynamics at a Quantum Critical Point
Universal Post-quench Dynamics at a Quantum Critical Point Peter P. Orth University of Minnesota, Minneapolis, USA Rutgers University, 10 March 2016 References: P. Gagel, P. P. Orth, J. Schmalian Phys.
More informationRenormalization of microscopic Hamiltonians. Renormalization Group without Field Theory
Renormalization of microscopic Hamiltonians Renormalization Group without Field Theory Alberto Parola Università dell Insubria (Como - Italy) Renormalization Group Universality Only dimensionality and
More informationLecture 2: Deconfined quantum criticality
Lecture 2: Deconfined quantum criticality T. Senthil (MIT) General theoretical questions Fate of Landau-Ginzburg-Wilson ideas at quantum phase transitions? (More precise) Could Landau order parameters
More informationPart III: Impurities in Luttinger liquids
Functional RG for interacting fermions... Part III: Impurities in Luttinger liquids 1. Luttinger liquids 2. Impurity effects 3. Microscopic model 4. Flow equations 5. Results S. Andergassen, T. Enss (Stuttgart)
More informationORBITAL SELECTIVITY AND HUND S PHYSICS IN IRON-BASED SC. Laura Fanfarillo
ORBITAL SELECTIVITY AND HUND S PHYSICS IN IRON-BASED SC Laura Fanfarillo FROM FERMI LIQUID TO NON-FERMI LIQUID Strong Correlation Bad Metal High Temperature Fermi Liquid Low Temperature Tuning parameter
More informationResistivity studies in magnetic materials. Makariy A. Tanatar
Resistivity studies in magnetic materials 590B Makariy A. Tanatar November 30, 2018 Classical examples Quantum criticality Nematicity Density waves: nesting Classics: resistivity anomaly at ferromagnetic
More informationPhase 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 informationThe mass of the Higgs boson
The mass of the Higgs boson LHC : Higgs particle observation CMS 2011/12 ATLAS 2011/12 a prediction Higgs boson found standard model Higgs boson T.Plehn, M.Rauch Spontaneous symmetry breaking confirmed
More informationRecent Developments in Holographic Superconductors. Gary Horowitz UC Santa Barbara
Recent Developments in Holographic Superconductors Gary Horowitz UC Santa Barbara Outline 1) Review basic ideas behind holographic superconductors 2) New view of conductivity and the zero temperature limit
More informationSpin or Orbital-based Physics in the Fe-based Superconductors? W. Lv, W. Lee, F. Kruger, Z. Leong, J. Tranquada. Thanks to: DOE (EFRC)+BNL
Spin or Orbital-based Physics in the Fe-based Superconductors? W. Lv, W. Lee, F. Kruger, Z. Leong, J. Tranquada Thanks to: DOE (EFRC)+BNL Spin or Orbital-based Physics in the Fe-based Superconductors?
More informationQuantum disordering magnetic order in insulators, metals, and superconductors
Quantum disordering magnetic order in insulators, metals, and superconductors Perimeter Institute, Waterloo, May 29, 2010 Talk online: sachdev.physics.harvard.edu HARVARD Cenke Xu, Harvard arxiv:1004.5431
More informationTrapping Centers at the Superfluid-Mott-Insulator Criticality: Transition between Charge-quantized States
Trapping Centers at the Superfluid-Mott-Insulator Criticality: Transition between Charge-quantized States Boris Svistunov University of Massachusetts, Amherst DIMOCA 2017, Mainz Institute for Theoretical
More informationSpin or Orbital-based Physics in the Fe-based Superconductors? W. Lv, W. Lee, F. Kruger, Z. Leong, J. Tranquada. Thanks to: DOE (EFRC)+BNL
Spin or Orbital-based Physics in the Fe-based Superconductors? W. Lv, W. Lee, F. Kruger, Z. Leong, J. Tranquada Thanks to: DOE (EFRC)+BNL Spin or Orbital-based Physics in the Fe-based Superconductors?
More informationKolloquium 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 informationDefining Chiral Gauge Theories Beyond Perturbation Theory
Defining Chiral Gauge Theories Beyond Perturbation Theory Lattice Regulating Chiral Gauge Theories Dorota M Grabowska UC Berkeley Work done with David B. Kaplan: Phys. Rev. Lett. 116 (2016), no. 21 211602
More informationRole of Incommensuration in the charge density wave and superconducting states of 1T-TiSe 2
Role of Incommensuration in the charge density wave and superconducting states of 1T-TiSe 2 Astha Sethi May 10, 2017 Abstract A brief review of some of the most recent experiments on the charge density
More informationAn imbalanced Fermi gas in 1 + ɛ dimensions. Andrew J. A. James A. Lamacraft
An imbalanced Fermi gas in 1 + ɛ dimensions Andrew J. A. James A. Lamacraft 2009 Quantum Liquids Interactions and statistics (indistinguishability) Some examples: 4 He 3 He Electrons in a metal Ultracold
More informationElectronic Liquid Crystal Phases in Strongly Correlated Systems
Electronic Liquid Crystal Phases in Strongly Correlated Systems Eduardo Fradkin University of Illinois at Urbana-Champaign Talk at the workshop Large Fluctuations and Collective Phenomena in Disordered
More informationInverse square potential, scale anomaly, and complex extension
Inverse square potential, scale anomaly, and complex extension Sergej Moroz Seattle, February 2010 Work in collaboration with Richard Schmidt ITP, Heidelberg Outline Introduction and motivation Functional
More informationSM, EWSB & Higgs. MITP Summer School 2017 Joint Challenges for Cosmology and Colliders. Homework & Exercises
SM, EWSB & Higgs MITP Summer School 017 Joint Challenges for Cosmology and Colliders Homework & Exercises Ch!"ophe Grojean Ch!"ophe Grojean DESY (Hamburg) Humboldt University (Berlin) ( christophe.grojean@desy.de
More informationThe Hubbard model in cold atoms and in the high-tc cuprates
The Hubbard model in cold atoms and in the high-tc cuprates Daniel E. Sheehy Aspen, June 2009 Sheehy@LSU.EDU What are the key outstanding problems from condensed matter physics which ultracold atoms and
More informationNon Fermi liquid effects in dense matter. Kai Schwenzer, Thomas Schäfer INT workshop From lattices to stars Seattle,
Non Fermi liquid effects in dense matter Kai Schwenzer, Thomas Schäfer INT workshop From lattices to stars Seattle, 27.5.2004 1 Introduction Possible phases at high density...... all involve condensed
More informationA brief Introduction of Fe-based SC
Part I: Introduction A brief Introduction of Fe-based SC Yunkyu Bang (Chonnam National Univ., Kwangju, Korea) Lecture 1: Introduction 1. Overview 2. What is sign-changing s-wave gap : +/-s-wave gap Lecture
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 informationPhase 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 informationVertex corrections for impurity scattering at a ferromagnetic quantum critical point
PHYSICAL REVIEW B 8, 5 Vertex corrections for impurity scattering at a ferromagnetic quantum critical point Enrico Rossi, * and Dirk K. Morr, Department of Physics, University of Illinois at Chicago, Chicago,
More informationBCS-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 informationMott metal-insulator transition on compressible lattices
Mott metal-insulator transition on compressible lattices Markus Garst Universität zu Köln T p in collaboration with : Mario Zacharias (Köln) Lorenz Bartosch (Frankfurt) T c Mott insulator p c T metal pressure
More information8.324 Relativistic Quantum Field Theory II
8.3 Relativistic Quantum Field Theory II MIT OpenCourseWare Lecture Notes Hong Liu, Fall 010 Lecture Firstly, we will summarize our previous results. We start with a bare Lagrangian, L [ 0, ϕ] = g (0)
More informationStrongly Correlated Physics With Ultra-Cold Atoms
Strongly Correlated Physics With Ultra-Cold Atoms Predrag Nikolić Rice University Acknowledgments Collaborators Subir Sachdev Eun-Gook Moon Anton Burkov Arun Paramekanti Sponsors W.M.Keck Program in Quantum
More informationRelativistic magnetotransport in graphene
Relativistic magnetotransport in graphene Markus Müller in collaboration with Lars Fritz (Harvard) Subir Sachdev (Harvard) Jörg Schmalian (Iowa) Landau Memorial Conference June 6, 008 Outline Relativistic
More informationCFT approach to multi-channel SU(N) Kondo effect
CFT approach to multi-channel SU(N) Kondo effect Sho Ozaki (Keio Univ.) In collaboration with Taro Kimura (Keio Univ.) Seminar @ Chiba Institute of Technology, 2017 July 8 Contents I) Introduction II)
More informationQCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV)
QCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV) 1 m N m ρ Λ QCD 0 m π m u,d In a generic physical system, there are often many scales involved. However, for a specific
More informationQuantum phase transitions
Quantum phase transitions Thomas Vojta Department of Physics, University of Missouri-Rolla Phase transitions and critical points Quantum phase transitions: How important is quantum mechanics? Quantum phase
More informationUniversal Dynamics from the Conformal Bootstrap
Universal Dynamics from the Conformal Bootstrap Liam Fitzpatrick Stanford University! in collaboration with Kaplan, Poland, Simmons-Duffin, and Walters Conformal Symmetry Conformal = coordinate transformations
More informationtheory, which can be quite useful in more complex systems.
Physics 7653: Statistical Physics http://www.physics.cornell.edu/sethna/teaching/653/ In Class Exercises Last correction at August 30, 2018, 11:55 am c 2017, James Sethna, all rights reserved 9.5 Landau
More informationElectronic quasiparticles and competing orders in the cuprate superconductors
Electronic quasiparticles and competing orders in the cuprate superconductors Andrea Pelissetto Rome Subir Sachdev Ettore Vicari Pisa Yejin Huh Harvard Harvard Gapless nodal quasiparticles in d-wave superconductors
More informationPhase diagram of the cuprates: Where is the mystery? A.-M. Tremblay
Phase diagram of the cuprates: Where is the mystery? A.-M. Tremblay I- Similarities between phase diagram and quantum critical points Quantum Criticality in 3 Families of Superconductors L. Taillefer,
More informationCritical lines and points. in the. QCD phase diagram
Critical lines and points in the QCD phase diagram Understanding the phase diagram Phase diagram for m s > m u,d quark-gluon plasma deconfinement quark matter : superfluid B spontaneously broken nuclear
More informationDR.RUPNATHJI( DR.RUPAK NATH )
11 Perturbation Theory and Feynman Diagrams We now turn our attention to interacting quantum field theories. All of the results that we will derive in this section apply equally to both relativistic and
More informationMODEL WITH SPIN; CHARGE AND SPIN EXCITATIONS 57
56 BOSONIZATION Note that there seems to be some arbitrariness in the above expressions in terms of the bosonic fields since by anticommuting two fermionic fields one can introduce a minus sine and thus
More informationDuality and Holography
Duality and Holography? Joseph Polchinski UC Davis, 5/16/11 Which of these interactions doesn t belong? a) Electromagnetism b) Weak nuclear c) Strong nuclear d) a) Electromagnetism b) Weak nuclear c) Strong
More informationManifestly diffeomorphism invariant classical Exact Renormalization Group
Manifestly diffeomorphism invariant classical Exact Renormalization Group Anthony W. H. Preston University of Southampton Supervised by Prof. Tim R. Morris Talk prepared for Asymptotic Safety seminar,
More informationLuigi 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 informationTransport w/o quasiparticles
Transport w/o quasiparticles Good metals, bad metals and insulators Sean Hartnoll (Stanford) -- Caneel Bay, Jan. 2013 Based on: 1201.3917 w/ Diego Hofman 1212.2998 w/ Aristos Donos (also work in progress
More informationNTNU Trondheim, Institutt for fysikk
NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory I Contact: Michael Kachelrieß, tel. 99890701 Allowed tools: mathematical tables Some formulas can be found on p.2. 1. Concepts.
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 informationQuasi-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 informationPhysics 212: Statistical mechanics II Lecture XI
Physics 212: Statistical mechanics II Lecture XI The main result of the last lecture was a calculation of the averaged magnetization in mean-field theory in Fourier space when the spin at the origin is
More informationDeconfined Quantum Critical Points
Deconfined Quantum Critical Points Leon Balents T. Senthil, MIT A. Vishwanath, UCB S. Sachdev, Yale M.P.A. Fisher, UCSB Outline Introduction: what is a DQCP Disordered and VBS ground states and gauge theory
More informationLandau-Fermi liquid theory
Landau- 1 Chennai Mathematical Institute April 25, 2011 1 Final year project under Prof. K. Narayan, CMI Interacting fermion system I Basic properties of metals (heat capacity, susceptibility,...) were
More informationHolographic superconductors
Holographic superconductors Sean Hartnoll Harvard University Work in collaboration with Chris Herzog and Gary Horowitz : 0801.1693, 0810.1563. Frederik Denef : 0901.1160. Frederik Denef and Subir Sachdev
More informationNew perspectives in superconductors. E. Bascones Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)
New perspectives in superconductors E. Bascones Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC) E. Bascones leni@icmm.csic.es Outline Talk I: Correlations in iron superconductors Introduction
More informationarxiv:cond-mat/ v1 4 Aug 2003
Conductivity of thermally fluctuating superconductors in two dimensions Subir Sachdev arxiv:cond-mat/0308063 v1 4 Aug 2003 Abstract Department of Physics, Yale University, P.O. Box 208120, New Haven CT
More informationSpectral action, scale anomaly. and the Higgs-Dilaton potential
Spectral action, scale anomaly and the Higgs-Dilaton potential Fedele Lizzi Università di Napoli Federico II Work in collaboration with A.A. Andrianov (St. Petersburg) and M.A. Kurkov (Napoli) JHEP 1005:057,2010
More informationEffective Field Theory
Effective Field Theory Iain Stewart MIT The 19 th Taiwan Spring School on Particles and Fields April, 2006 Physics compartmentalized Quantum Field Theory String Theory? General Relativity short distance
More informationNon equilibrium Ferromagnetism and Stoner transition in an ultracold Fermi gas
Non equilibrium Ferromagnetism and Stoner transition in an ultracold Fermi gas Gareth Conduit, Ehud Altman Weizmann Institute of Science See: Phys. Rev. A 82, 043603 (2010) and arxiv: 0911.2839 Disentangling
More information