Qu-Transitions. P. Coleman (CMT, Rutgers) IIT Kanpur Feb 7, 2010.

Transcription

1 Qu-Transitions P. Coleman (CMT, Rutgers) IIT Kanpur Feb 7, 2010.

2 Qu-Transitions Phase transitions in the quantum era P. Coleman (CMT, Rutgers) IIT Kanpur Feb 7, 2010.

3 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality New Ideas: breakup of the electron. Qu-frustration.

4 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality New Ideas: breakup of the electron. Qu-frustration.

5 1758 in Paris: 72 years after Principia

6 1758 in Paris: 72 years after Principia Classical revolution is still in full sway.

7 1758 in Paris: 72 years after Principia Classical revolution is still in full sway. Return of Halley s comet. Publishers in Paris decide to bring out the 1st French Translation of Newton s Principia, which they have held in proof form for ten years.

8 1758 in Paris: 72 years after Principia Classical revolution is still in full sway. Return of Halley s comet. Publishers in Paris decide to bring out the 1st French Translation of Newton s Principia, which they have held in proof form for ten years.

9 1758 in Paris: 72 years after Principia Classical revolution is still in full sway. Marquise Emilie du Châtelet ( ) Mathematical Physicist: Translator and interpreter of Principia. "ce beau probleme astronomico-geometrique"

10 1758 in Paris: 72 years after Principia Classical revolution is still in full sway. Marquise Emilie du Châtelet ( ) Mathematical Physicist: Translator and interpreter of Principia. "ce beau probleme astronomico-geometrique" du Chatelet reviews the conflicting world views of Leibniz and Newton.

11 1758 in Paris: 72 years after Principia Classical revolution is still in full sway. Marquise Emilie du Châtelet ( ) Mathematical Physicist: Translator and interpreter of Principia. "ce beau probleme astronomico-geometrique" du Chatelet reviews the conflicting world views of Leibniz and Newton. Newtons Momentum i m i v i Leibniz vis vivre m i (v i ) 2 i

12 1758 in Paris: 72 years after Principia Classical revolution is still in full sway. Marquise Emilie du Châtelet ( ) Mathematical Physicist: Translator and interpreter of Principia. "ce beau probleme astronomico-geometrique" du Chatelet reviews the conflicting world views of Leibniz and Newton. Newtons Momentum i m i v i Leibniz vis vivre m i (v i ) 2 Resolution of the controversy (and the missing factor of a half) required a further years. i

13 108 years after Planck, many surprises later, the quantum era is in full sway.

14 108 years after Planck, many surprises later, the quantum era is in full sway.! T With a heavy heart, I have been converted to the idea that Fermi -Dirac, not Einstein-Bose is the correct statistics. I wish to write a short note on its application to paramagnetism. W. Pauli, in letter to Schrödinger, Dec 1926.

15 108 years after Planck, many surprises later, the quantum era is in full sway.

16 108 years after Planck, many surprises later, the quantum era is in full sway. Qubit

17 108 years after Planck, many surprises later, the quantum era is in full sway. Qubit Qu-information

18 108 years after Planck, many surprises later, the quantum era is in full sway. David Pines in musicofthequantum.rutgers.edu

19 Quantum zero point fluctuations:

20 Quantum zero point fluctuations: major unsolved problem of the quantum era.

21 Quantum zero point fluctuations: major unsolved problem of the quantum era. 73% of the mass of the cosmos is Dark Energy : an unidentified form of zero point energy, causing the expansion to accelerate.

22 Quantum zero point fluctuations: major unsolved problem of the quantum era. Zero point fluctuations profoundly transform matter, endowing it with marked tendency to develop new forms of order.

23 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality New Ideas: breakup of the electron. Qu-frustration.

24 Classical Criticality Custers et al (2002)

25 Classical Criticality Custers et al (2002)

26 Classical Criticality Custers et al (2002) Classical Critical Point

27 Classical Criticality Custers et al (2002) Classical Critical Point Oxygen. (Voronel et al 1963).

28 Classical Criticality Custers et al (2002) Michael Fisher New insights into physics often come from revisiting areas once thought to be closed. Michael Fisher. Classical Critical Point Oxygen. (Voronel et al 1963).

29 Classical Criticality Custers et al (2002) Michael Fisher Leo Kadanoff Ben Widom Anatoly Larkin Ken Wilson New insights into physics often come from revisiting areas once thought to be closed. Michael Fisher. Classical Critical Point Oxygen. (Voronel et al 1963).

30 Classical Criticality Custers et al (2002) Michael Fisher Leo Kadanoff Ben Widom Anatoly Larkin Ken Wilson New insights into physics often come from revisiting areas once thought to be closed. Michael Fisher. Classical Critical Point 20th Century Revolution Oxygen. (Voronel et al 1963).

31 Classical Criticality Custers et al (2002) Michael Fisher Leo Kadanoff Ben Widom Anatoly Larkin Ken Wilson New insights into physics often come from revisiting areas once thought to be closed. Michael Fisher. Classical Critical Point Critical matter 20th Century Revolution

32 Classical Criticality Custers et al (2002) Michael Fisher Leo Kadanoff Ben Widom Anatoly Larkin Ken Wilson New insights into physics often come from revisiting areas once thought to be closed. Michael Fisher. Classical Critical Point Critical matter - universal 20th Century Revolution

33 Quantum Phase-Transition Custers et al (2002)

34 Quantum Phase-Transition Phase transition driven by zero point motion. Custers et al (2002)

35 Quantum Phase-Transition Phase transition driven by zero point motion. [H, ψ] = 0 Custers et al (2002) ψ = S even S odd..

36 Quantum Phase-Transition Phase transition driven by zero point motion. [H, ψ] = 0 Custers et al (2002) ψ = S even S odd.. Quantum Fluctuations

37 Quantum Phase-Transition Phase transition driven by zero point motion. [H, ψ] = 0 Custers et al (2002) ψ = S even S odd.. Quantum Fluctuations What happens when the time and length scale of zero point quantum fluctuations diverges?

38 Quantum Phase-Transition Phase transition driven by zero point motion. [H, ψ] = 0 Custers et al (2002) ψ = S even S odd.. Quantum Fluctuations QCP What happens when the time and length scale of zero point quantum fluctuations diverges?

39 Quantum Phase-Transition Phase transition driven by zero point motion. [H, ψ] = 0 Custers et al (2002) ψ = S even S odd.. Quantum Critical matter Quantum Fluctuations QCP What happens when the time and length scale of zero point quantum fluctuations diverges?

40 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality New Ideas: breakup of the electron. Qu-frustration.

41 Landau: interactions can be turned on adiabatically, preserving the excitation spectrum.

42 Landau: interactions can be turned on adiabatically, preserving the excitation spectrum. Quasiparticle - Interactions adiabatically -

43 Landau: interactions can be turned on adiabatically, preserving the excitation spectrum. Quasiparticle - Interactions adiabatically - quasi-particle quasi-hole

44 Landau: interactions can be turned on adiabatically, preserving the excitation spectrum. Quasiparticle - Interactions adiabatically - quasi-particle quasi-hole Landau, JETP 3, 920 (1957)

45 He-3 (1950/60s) (Fairbanks, many others) Landau: interactions can be turned on adiabatically, preserving the excitation spectrum. Quasiparticle - Interactions adiabatically - quasi-particle quasi-hole Landau, JETP 3, 920 (1957)

46 Landau s Question.

47 Landau s Question. Larkin Dyson Landau Abrikosov

48 Landau s Question. Larkin Dyson Landau Abrikosov Peierls

49 Landau s Question. Larkin Dyson Landau Abrikosov But what happens when the interaction becomes too large? Peierls

50 0 Fermi Liquid X~U/t But what happens when the interaction becomes too large?

51 0 Fermi Liquid Xc Long range order X~U/t Landau 1936 But what happens when the interaction becomes too large? Electrons order

52 0 Fermi Liquid Xc Long range order X~U/t But what happens when the interaction becomes too large? Landau 1936 Peierls/Mott 1939 Electrons order Electrons localize

53 0 Fermi Liquid Xc Long range order X~U/t But what happens when the interaction becomes too large? Landau 1936 Peierls/Mott 1939 Anderson 1961 Electrons order Electrons localize Moments form

54 T Strange Metal QCP Hertz, 1976 Long range order X~U/t 0 Fermi Liquid Xc But what happens when the interaction becomes too large? Landau 1936 Peierls/Mott 1939 Anderson 1961 Electrons order Electrons localize Moments form

55 Takagi et al, PRL 92 Avoided Criticality T(K) Cuprates Tc=11-92K

56 Takagi et al, PRL 92 Avoided Criticality Pseudogap metal T(K) T T* Marginal Fermi liquid Cuprates Tc=11-92K AFM Quantum critical point Fermi liquid x

57 Takagi et al, PRL 92 Avoided Criticality T(K) Pseudogap metal T T* Tuson Park, (2007). Marginal Fermi liquid Cuprates Tc=11-92K AFM Quantum critical point Fermi liquid x Data: Tuson Park Figure rendition: Mathias Graf

58 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality New Ideas: breakup of the electron. Qu-frustration.

59 Kondo effect

60 Kondo effect (a digression)

61 Kondo effect (a digression) Kondo Kondo KHR-2 HV, the robot that plays soccer, fights with other bots and dances salsa

62 Kondo effect (a digression) T

63 Kondo effect (a digression) A 75 year odyssey T

64 Kondo effect (a digression) Kondo (1962) Fe Kondo Temperature A 75 year odyssey T

65 Kondo effect (a digression) Kondo (1962) Fe Spins asymptotically free Kondo Temperature A 75 year odyssey T

66 Kondo effect (a digression) Kondo (1962) + Spins asymptotically free Kondo Temperature +

67 Kondo effect (a digression) Kondo (1962) + Spins asymptotically free Kondo Temperature - +

68 Kondo effect (a digression) Kondo (1962) + Spins asymptotically free Spins absorbed into singlet ground-state Kondo Temperature - + Nozieres Local Fermi liquid (Nozieres 76)

69 Kondo effect (a digression) Kondo (1962) + Spins asymptotically free Spins absorbed into singlet ground-state - + χ 1 T K T K Kondo Temperature χ 1/T Nozieres Local Fermi liquid (Nozieres 76) T K T

70 DONIACH S Hypothesis. Doniach (1977) Kondo Lattice Model (Kasuya, 1951)

71 DONIACH S Hypothesis. Doniach (1977) Kondo Lattice Model (Kasuya, 1951)

72 DONIACH S Hypothesis. Doniach (1977) Kondo Lattice Model (Kasuya, 1951)

73 DONIACH S Hypothesis. Doniach (1977) Kondo Lattice Model (Kasuya, 1951)

74 DONIACH S Hypothesis. Doniach (1977) Kondo Lattice Model (Kasuya, 1951) T K = D exp[ 1/2Jρ] The main result... is that there should be a second-order transition > at zero temperature, as the exchange coupling is varied, between an antiferromagnetic ground state for weak J and a Kondo-like state in which the local moments are quenched. QC

75 DONIACH S Hypothesis. Doniach (1977) Kondo Lattice Model (Kasuya, 1951) T K = D exp[ 1/2Jρ] The main result... is that there should be a second-order transition > at zero temperature, as the exchange coupling is varied, between an antiferromagnetic ground state for weak J and a Kondo-like state in which the local moments are quenched. QC

76 DONIACH S Hypothesis. Doniach (1977) Kondo Lattice Model (Kasuya, 1951) T K = D exp[ 1/2Jρ] Large Fermi surface of composite Fermions QC >

77 DONIACH S Hypothesis. Doniach (1977) Kondo Lattice Model (Kasuya, 1951) T K = D exp[ 1/2Jρ] Large Fermi surface of composite Fermions QC ? >

78 T 0 Fermi Liquid QCP Xc Long range order X~U/t

79 T 0 Fermi Liquid QCP Xc Moments form Long range order X~U/t

80 T 0 Fermi Liquid QCP Xc Moments form Long range order J ~ 1/U X~U/t

81 T J ~ 1/U QCP Moments form Long range order X~U/t 0 Fermi Liquid Xc J ~ 1/U

82 T J ~ 1/U QCP Moments form Long range order X~U/t 0 Fermi Liquid Xc J ~ 1/U T K = D exp[ 1/2Jρ] QCP

83 TK = D exp[ 1/2Jρ] T J ~ 1/U QCP Moments form Long range order X~U/t 0 Fermi Liquid Xc J ~ 1/U QCP

84 Heavy Fermion Metals Review: cond-mat/ UBe 13

85 Heavy Fermion Metals Review: cond-mat/ UBe 13

86 Heavy Fermion Metals Review: cond-mat/ UBe 13 Coherent Heavy Fermi Liquid

87 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality: New Ideas: breakup of the electron. Qu-frustration. Experiments

88 Quantum Criticality: divergent specific heat capacity H. Von Lohneyson (1996) Heavy Fermion Materials AFM metal P c P Quantum Critical Point

89 Quantum Criticality: divergent specific heat capacity H. Von Lohneyson (1996) Heavy Fermion Materials AFM metal P c P Quantum Critical Point

90 Quantum Criticality: divergent specific heat capacity H. Von Lohneyson (1996) Heavy Fermion Materials AFM metal P c P Quantum Critical Point

91 Divergence of Interaction and Effective Mass Gegenwart et al (2002) T-Linear T-Linear T 2 T 2 T 2

92 Divergence of Interaction and Effective Mass Gegenwart et al (2002) T-Linear T-Linear T 2 T 2 T 2

93 How do fermions get heavy and die? PC, Pepin, Si and Ramazashvili, J. Cond Matt.,13}, R723 (2001). anticipated an abrupt change in FS when a composite heavy electron undergoes a Kondo breakdown.

94 S. Paschen et al, Nature 432, 881 (2004)

95 S. Paschen et al, Nature 432, 881 (2004) Jump in the Hall constant at a field tuned QCP.

96 Reconstruction of the Fermi Surface and mass divergence CeRhIn5 Tuson Park, (2007). Data: Tuson Park Figure rendition: Mathias Graf

97 Reconstruction of the Fermi Surface and mass divergence CeRhIn5 Tuson Park, (2007). Data: Tuson Park Figure rendition: Mathias Graf

98 Reconstruction of the Fermi Surface and mass divergence CeRhIn5 Tuson Park, (2007). Data: Tuson Park Figure rendition: Mathias Graf Shishido et al (2006)

99 Reconstruction of the Fermi Surface and mass divergence CeRhIn5 Tuson Park, (2007). Data: Tuson Park Figure rendition: Mathias Graf Shishido et al (2006)

100 Reconstruction of the Fermi Surface and mass divergence CeRhIn5 Tuson Park, (2007). Data: Tuson Park Figure rendition: Mathias Graf Shishido et al (2006)

101 Reconstruction of the Fermi Surface and mass divergence CeRhIn5 Tuson Park, (2007). Data: Tuson Park Figure rendition: Mathias Graf Shishido et al (2006)

102 Reconstruction of the Fermi Surface and mass divergence CeRhIn5 Tuson Park, (2007). Data: Tuson Park Figure rendition: Mathias Graf Shishido et al (2006)

103 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality: New Ideas: breakup of the electron. Black hole in the phase diagram Qu-frustration.

104 Black Hole in the Phase Diagram. Zachary Fisk

105 Black Hole in the Phase Diagram. AFM metal Zachary Fisk P c P

106 Black Hole in the Phase Diagram. AFM metal Zachary Fisk P c P

107 Black Hole in the Phase Diagram. AFM metal Zachary Fisk P c P P.C and A. Schofield, Nature (2005)

108 Black Hole in the Phase Diagram. AFM metal Zachary Fisk P c P \ PHASE HORIZON P.C and A. Schofield, Nature (2005)

109 Black Hole in the Phase Diagram. AFM metal Zachary Fisk N P c P \ PHASE HORIZON P.C and A. Schofield, Nature (2005)

110 Black Hole in the Phase Diagram. AFM metal Zachary Fisk D P c P \ PHASE HORIZON P.C and A. Schofield, Nature (2005)

111 Black Hole in the Phase Diagram. AFM metal Zachary Fisk A P c P \ PHASE HORIZON P.C and A. Schofield, Nature (2005)

112 Black Hole in the Phase Diagram. AFM metal Zachary Fisk A P c P \ PHASE HORIZON P.C and A. Schofield, Nature (2005) John Hertz: Critical droplet is Quantum if

113 Feynman Hertz

114 Feynman Hertz

115 Feynman Hertz Temperature: Boundary condition in time. Sachdev (1999), Continentino (2001), Palova (2009).

116 Feynman Hertz Temperature: Boundary condition in time. Sachdev (1999), Continentino (2001), Palova (2009). AFM metal P c P

117 Feynman Hertz Temperature: Boundary condition in time. Sachdev (1999), Continentino (2001), Palova (2009). Quantum Critical Bubble AFM metal P c P

118 Feynman Hertz Temperature: Boundary condition in time. Sachdev (1999), Continentino (2001), Palova (2009). Quantum Critical Bubble AFM metal P c P

119 Feynman Hertz Temperature: Boundary condition in time. Sachdev (1999), Continentino (2001), Palova (2009). Quantum Critical Bubble (Q) Quantum critical region: interior of correlation bubble. AFM metal (Q) P c P

120 Feynman Hertz Temperature: Boundary condition in time. Sachdev (1999), Continentino (2001), Palova (2009). Quantum Critical Bubble (Q) Quantum critical region: interior of correlation bubble. (P) Paramagnet: probes exterior of correlation bubble AFM metal (Q) P c (P) P

121 Feynman Hertz Temperature: Boundary condition in time. Sachdev (1999), Continentino (2001), Palova (2009). Quantum Critical Bubble (Q) Quantum critical region: interior of correlation bubble. (P) Paramagnet: probes exterior of correlation bubble AFM metal (Q) Quantum Critical Bubble P c (P) P

122 Feynman Hertz Temperature: Boundary condition in time. Sachdev (1999), Continentino (2001), Palova (2009). Quantum Critical Bubble (Q) Quantum critical region: interior of correlation bubble. (P) Paramagnet: probes exterior of correlation bubble AFM metal (Q) Quantum Critical Bubble P c (P) P

123 E/T Scaling: M. C. Aronson et al, PRL 75, 725 (1995). Meigan Aronson

124 E/T Scaling: M. C. Aronson et al, PRL 75, 725 (1995). Meigan Aronson

125 E/T Scaling: M. C. Aronson et al, PRL 75, 725 (1995). Meigan Aronson Almut Schroeder CeCu 6-x Au x (x=0.1) Schroeder et al, Nature 407,351 (2000).

126 E/T Scaling: M. C. Aronson et al, PRL 75, 725 (1995). Meigan Aronson Almut Schroeder Physics Below the upper Critical Dimension. CeCu 6-x Au x (x=0.1) Schroeder et al, Nature 407,351 (2000).

127 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality: New Ideas: breakup of the electron. Qu-frustration. Failure of the Standard model

128 Standard Model: Quantum SDW? Moriya Doniach Schrieffer Hertz Millis Moriya, Doniach, Schrieffer (60s) Hertz (76) Millis (93) Fermi Surface F.S. instability

129 Standard Model: Quantum SDW? Moriya Doniach Schrieffer Hertz Millis Moriya, Doniach, Schrieffer (60s) Hertz (76) Millis (93) Fermi Surface vertex nonsingular F.S. instability

130 Standard Model: Quantum SDW? Moriya Doniach Schrieffer Hertz Millis Moriya, Doniach, Schrieffer (60s) Hertz (76) Millis (93) Fermi Surface vertex nonsingular F.S. instability

131 Standard Model: Quantum SDW? Moriya Doniach Schrieffer Hertz Millis Moriya, Doniach, Schrieffer (60s) Hertz (76) Millis (93) Fermi Surface vertex nonsingular Time counts as z =2 scaling dimensions F.S. instability

132 Standard Model: Quantum SDW? Moriya Doniach Schrieffer Hertz Millis Moriya, Doniach, Schrieffer (60s) Hertz (76) Millis (93) Fermi Surface vertex nonsingular If d + z = d + 2 > 4 : " 4 terms irrelevent Critical modes are Gaussian. T is not the only energy scale. Time counts as z =2 scaling dimensions F.S. instability

133 Singular potential is rapidly modulated: only affects electrons along hot-lines. Predicts: Landau s Fermi Liquid Should Survive at a Quantum Critical Point.

134 Q Singular potential is rapidly modulated: only affects electrons along hot-lines. Predicts: Landau s Fermi Liquid Should Survive at a Quantum Critical Point.

135 Q Singular potential is rapidly modulated: only affects electrons along hot-lines. k k-q q Predicts: Landau s Fermi Liquid Should Survive at a Quantum Critical Point.

136 divergent Q Singular potential is rapidly modulated: only affects electrons along hot-lines. k k-q q Predicts: Landau s Fermi Liquid Should Survive at a Quantum Critical Point.

137 divergent Q finite Singular potential is rapidly modulated: only affects electrons along hot-lines. k k-q q Predicts: Landau s Fermi Liquid Should Survive at a Quantum Critical Point.

138 divergent Q finite Singular potential is rapidly modulated: only affects electrons along hot-lines. k k-q q Predicts: Landau s Fermi Liquid Should Survive at a Quantum Critical Point.

139 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality New Ideas: breakup of the electron. Qu-frustration.

140 New Ideas

141 New Ideas Si, Ingersent H Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode, Fluctuations critical in time. t Requires a two dimensional spin fluid

142 New Ideas Si, Ingersent H Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode, Fluctuations critical in time. t Requires a two dimensional spin fluid Locality of critical fluctuations Schroeder et al, Nature 407,351(2000). T.0.75 (K 0.75 )

143 New Ideas Si, Ingersent H Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode, Fluctuations critical in time. t Requires a two dimensional spin fluid

144 New Ideas Si, Ingersent H Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode, Fluctuations critical in time. t Requires a two dimensional spin fluid Deconfined Criticality: Two diverging lengthscales. (Hermele et al 2004; Senthil et al, Science 2004). Critical Matter Free spinons Magnetic order Senthil Sachdev Vishwanath

145 New Ideas Si, Ingersent H Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode, Fluctuations critical in time. t Requires a two dimensional spin fluid Deconfined Criticality: Two diverging lengthscales. (Hermele et al 2004; Senthil et al, Science 2004). Senthil Sachdev Vishwanath

146

147 P. Gegenwart, T. Westerkamp et al., Science 315, 5814 (2007)

148 New Ideas Large N Approaches. (PC et al JCM, 2001, Rech et al 2005, Lebanon et al 2006, Pepin 2006, 2008, Paul Pepin, Norman 2008). Pepin

149 New Ideas S[ψ] τ,x ψ(x, τ) Wild quantum fluctuations! Large N Approaches. (PC et al JCM, 2001, Rech et al 2005, Lebanon et al 2006, Pepin 2006, 2008, Paul Pepin, Norman 2008). Pepin

150 New Ideas S[ψ] τ,x ψ(x, τ) Wild quantum fluctuations! Large N limit Large N Approaches. (PC et al JCM, 2001, Rech et al 2005, Lebanon et al 2006, Pepin 2006, 2008, Paul Pepin, Norman 2008). Pepin

151 New Ideas S[ψ] τ,x ψ(x, τ) Wild quantum fluctuations! Large N limit Large N Approaches. (PC et al JCM, 2001, Rech et al 2005, Lebanon et al 2006, Pepin 2006, 2008, Paul Pepin, Norman 2008). Pepin

152 New Ideas S[ψ] τ,x ψ(x, τ) 1 N eff Large N limit Large N Approaches. (PC et al JCM, 2001, Rech et al 2005, Lebanon et al 2006, Pepin 2006, 2008, Paul Pepin, Norman 2008). Pepin

153 New Ideas S[ψ] τ,x ψ(x, τ) 1 N eff Large N limit Large N Approaches. (PC et al JCM, 2001, Rech et al 2005, Lebanon et al 2006, Pepin 2006, 2008, Paul Pepin, Norman 2008). Pepin

154 New Ideas S[ψ] τ,x ron Holon Spinon Electron 1 N eff classical path ψ(x, τ) Large N limit Large N Approaches. (PC et al JCM, 2001, Rech et al 2005, Lebanon et al 2006, Pepin 2006, 2008, Paul Pepin, Norman 2008). Pepin

155 New Ideas M Cubrovic, J Zaanen, K Schalm - Science, 2009 Zaanen Liu McGreevy S[ψ] τ,x ron Holon Spinon Electron 1 N eff classical path ψ(x, τ) Large N limit Large N Approaches. (PC et al JCM, 2001, Rech et al 2005, Lebanon et al 2006, Pepin 2006, 2008, Paul Pepin, Norman 2008). Pepin

156 Qu-era: revolutions always have a second part. Classical vs quantum criticality. Peierls question. Heavy electron Quantum Criticality New Ideas: breakup of the electron. Qu-frustration.

157 Qu- frustration Frustration and Kondo have different effects.

158 Qu- frustration Frustration and Kondo have different effects. AFM Large FS Heavy Fermi Liquid K ~ TK/JH

159 Qu- frustration Frustration and Kondo have different effects. Q Spin Liquid AFM

160 Qu- frustration Frustration and Kondo have different effects. Q Spin Liquid AFM Large FS Heavy Fermi Liquid K ~ TK/JH

161 Qu- frustration Frustration and Kondo have different effects. Q Spin Liquid metal AFM Large FS Heavy Fermi Liquid K ~ TK/JH

162 Experimental Support S. Nakatsuji et al, Nature Physics (2008).!-YbAlB 4 SLM f~1/s AFM Large FS Heavy Fermi Liquid Doniach TK/JH

163 Experimental Support S. Nakatsuji et al, Nature Physics (2008).!-YbAlB 4 SLM f~1/s AFM Large FS Heavy Fermi Liquid Doniach TK/JH

164 Experimental Support S. Nakatsuji et al, Nature Physics (2008).!-YbAlB 4 SLM Non-Fermi liquid at B=0. Small field restores Fermi liquid behavior. f~1/s AFM Large FS Heavy Fermi Liquid Doniach TK/JH

165 Experimental Support S. Nakatsuji et al, Nature Physics (2008).!-YbAlB 4 SLM Non-Fermi liquid at B=0. Small field restores Fermi liquid behavior. f~1/s AFM Large FS Heavy Fermi Liquid Critical Phase? Doniach TK/JH

166 Experimental Support S. Nakatsuji et al, Nature Physics (2008).!-YbAlB 4 SLM Non-Fermi liquid at B=0. Small field restores Fermi liquid behavior. f~1/s AFM? Large FS Heavy Fermi Liquid Doniach TK/JH Critical Phase? See: A. Nevidomskyy & PC PRL (2009). T. Senthil, S.Sachdev, M.Vojta,PRL 90, ; PRB 69, (2004); P. W.Anderson, arxiv: (2008)

167 Experimental Support II SLM Canfield et al (unpublished) Q AFM Large FS Heavy Fermi Liquid K ~ TK/JH

168 Experimental Support II SLM Canfield et al (unpublished) Q AFM Large FS Heavy Fermi Liquid K ~ TK/JH

169 Experimental Support II SLM Canfield et al (unpublished) Q AFM Large FS Heavy Fermi Liquid K ~ TK/JH

170 Conclusions.

171 Conclusions. Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.

172 Conclusions. Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom. Fermi surface expansion and the loss of AFM need not coincide.

173 Conclusions. Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom. Fermi surface expansion and the loss of AFM need not coincide. Introduction of the frustration axis permits a unified treatment of spin liquid and Kondo effects.

174 Conclusions. Frustration 1/S Spin Liquid metal AFM Large FS Heavy Fermi Liquid Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom. Fermi surface expansion and the loss of AFM need not coincide. Doniach TK/JH Introduction of the frustration axis permits a unified treatment of spin liquid and Kondo effects.

175 Conclusions. Frustration 1/S Spin Liquid metal AFM Large FS Heavy Fermi Liquid Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom. Fermi surface expansion and the loss of AFM need not coincide. Doniach TK/JH Introduction of the frustration axis permits a unified treatment of spin liquid and Kondo effects. Spin liquid Kondo states may have been observed in three Yb heavy electron systems. More experiments needed.

176 Conclusions. Frustration 1/S Spin Liquid metal AFM Large FS Heavy Fermi Liquid Doniach TK/JH Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom. Fermi surface expansion and the loss of AFM need not coincide. Introduction of the frustration axis permits a unified treatment of spin liquid and Kondo effects. Spin liquid Kondo states may have been observed in three Yb heavy electron systems. More experiments needed.

177 Collaborators Flint Nev. Dzero Rech Lebanon Rebecca Flint Rutgers Andriy Nevidomskyy Rutgers Maxim Dzero U. Maryland Jerome Rech, CNRS, Marseille Eran Lebanon, Israel. Indranil Paul, CNRS, Grenoble Lucia Palova Rutgers Premi Chandra Rutgers Gergely Zarand Budapest Olivier Parcollet SpHT Paris. Andy Schofield Birmingham Qimiao Si Rice, Houston Catherine Pepin SpHT Paris. Almut Schroeder Kent State Gabriel Aeppli LCN Hilbert v. Lohneysen Karlsruhe 51 37