qu-transitionscoleman/talks/kanpur_colloq2010... · 2013. 10. 8. · criticality - universal...

Qu-Transitions

P. Coleman(CMT, Rutgers)

IIT KanpurFeb 7, 2010.

Friday, February 12, 2010

Qu-Transitions“Phase transitions in the quantum era”

P. Coleman(CMT, Rutgers)

IIT KanpurFeb 7, 2010.


• 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.

http://physics.rutgers.edu/talks/kanpurcolloq09.pdf


http://harpsichord.rutgers.edu/talks/issp_colloq09.pdf

http://harpsichord.rutgers.edu/talks/issp_colloq09.pdf


• Qu-era: revolutions always have a second part.


1758 in Paris: 72 years after “Principia”


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.

Classical revolution is still in full sway.



Marquise Emilie du Châtelet(1707-1749)

Mathematical Physicist:Translator and interpreter of Principia.


"ce beau probleme astronomico-geometrique"





du Chatelet reviews the conflicting world views of Leibniz and Newton.








�

i

mi(vi)2�

i

mi�vi

Newtons Momentum Leibniz’ “vis vivre”








�

i

mi(vi)2�

i

mi�vi

Newtons Momentum Leibniz’ “vis vivre”

Resolution of the controversy (and the missingfactor of a half) required a further 60-80 years.




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


“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.

!

T




Qubit



Qubit

Qu-information


David Pines in musicofthequantum.rutgers.edu



http://musicofthequantum.rutgers.edu

http://musicofthequantum.rutgers.edu

Quantum zero point fluctuations:


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.

major unsolved problem of the quantum era.



•Zero point fluctuationsprofoundly transformmatter, endowing it with markedtendency to develop new forms oforder.

major unsolved problem of the quantum era.



• Classical vs quantum criticality.


Classical Criticality

Custers et al (2002)




Classical Critical Point




Oxygen. (Voronel et al 1963).



“New insights into physics often come from revisiting areas once thought to be closed.” Michael Fisher.




Michael Fisher







Michael Fisher


Anatoly LarkinBen WidomLeo Kadanoff Ken Wilson






Michael Fisher



“20th Century Revolution”




Michael Fisher

Critical matter








Michael Fisher

Critical matter



- universal




Quantum Phase-Transition





Phase transition driven by zero point motion.




[H,ψ] �= 0

.

ψ =��

Seven − Sodd

�

.





[H,ψ] �= 0

Quantum Fluctuations

.

ψ =��

Seven − Sodd

�

.





[H,ψ] �= 0


.

ψ =��

Seven − Sodd

�

.


What happens when the timeand length scale of zero point quantum fluctuations diverges?




[H,ψ] �= 0


QCP

.

ψ =��

Seven − Sodd

�

.






[H,ψ] �= 0


QCP

.

ψ =��

Seven − Sodd

�

.


Quantum Critical matter




• Peierls’ question.


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



- Interactionsadiabatically

-

“Quasiparticle”




-

“Quasiparticle”

quasi-particle

quasi-hole


Landau, JETP 3, 920 (1957)



-

“Quasiparticle”

quasi-particle

quasi-hole


Landau, JETP 3, 920 (1957)

He-3 (1950/60s)(Fairbanks, many others) Landau: interactions can be turned on

adiabatically, preserving the excitation spectrum.


-

“Quasiparticle”

quasi-particle

quasi-hole


Landau’s Question.



Landau

DysonLarkin

Abrikosov



Landau

DysonLarkin

Abrikosov

Peierls



Landau

DysonLarkin

Abrikosov

PeierlsBut what happens when the interaction becomes too large?


0Fermi Liquid

X~U/t

But what happens when the interaction becomes too large?


0Fermi Liquid

“Electrons order”

Landau 1936

X~U/t

Xc

Long range order



0Fermi Liquid


Landau 1936

X~U/t

Xc

Long range order


“Electrons localize”

Peierls/Mott 1939


0Fermi Liquid


Landau 1936

“Moments form”

Anderson 1961

X~U/t

Xc

Long range order



Peierls/Mott 1939


0Fermi Liquid


Landau 1936

“Moments form”

Anderson 1961

X~U/t

Xc

Strange MetalT

“QCP”

Hertz, 1976

Long range order



Peierls/Mott 1939


Cuprates Tc=11-92K

T(K)0 200 400 600 800 1000

0.0

0.2

0.4

0.6

0.8

1.0

Takagi et al, PRL ‘92

“Avoided Criticality”


Cuprates Tc=11-92K

T(K)0 200 400 600 800 1000

0.0

0.2

0.4

0.6

0.8

1.0


x

Marginal Fermi liquid

Quantum critical point

Pseudogapmetal

Fermi liquid

T T*

AFM



Cuprates Tc=11-92K

T(K)0 200 400 600 800 1000

0.0

0.2

0.4

0.6

0.8

1.0


x

Marginal Fermi liquid

Quantum critical point

Pseudogapmetal

Fermi liquid

T T*

AFM


Data: Tuson ParkFigure rendition: Mathias Graf

Tuson Park, (2007).



• Heavy electron Quantum Criticality


Kondo effect


Kondo effect (a digression)



“Kondo”

Kondo KHR-2 HV, the robot that plays soccer, fights with other bots and dances salsa


Kondo effect

T

(a digression)


Kondo effect

T

“A 75 year odyssey”

(a digression)


Kondo effect

Kondo (1962)

T


“Kondo Temperature”

(a digression)

Fe


Kondo effect

Kondo (1962)

Spins asymptotically free

T



(a digression)

Fe



Kondo (1962)+ .....


+



-


Kondo (1962)+ .....


+



-


Kondo (1962)+ .....


“Nozieres Local Fermi liquid” (Nozieres 76)

+

“Kondo Temperature”Spins absorbed into singlet ground-state


-


Kondo (1962)+ .....


“Nozieres Local Fermi liquid” (Nozieres 76)

+


χ ∼ 1/T

χ TK

T

1TK

TK

Spins absorbed into singlet ground-state


Kondo Lattice Model(Kasuya, 1951)

DONIACH’SHypothesis.Doniach (1977)




>

TK = D exp[−1/2Jρ]

QC

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.Friday, February 12, 2010



>


QC

Large Fermi surface of composite Fermions

+

+

++

+

++

+

++

+

+++ +




>


QC

Large Fermi surface of composite Fermions

+

+

++

+

++

+

++

+

+++ +

?


0Fermi Liquid

X~U/t

Xc

T

“QCP”Long range order


0Fermi Liquid

X~U/t

Xc

T


“Moments form”


0Fermi Liquid

X~U/t

Xc

T


J ~ 1/U

“Moments form”


0Fermi Liquid

X~U/t

Xc

T


J ~ 1/U

“Moments form”

J ~ 1/U



0Fermi Liquid

X~U/t

Xc

T


J ~ 1/U

QCP

“Moments form”

J ~ 1/U


TK=Dexp[−1/2Jρ]

0Fermi Liquid

X~U/t

Xc

T


J ~ 1/U

QCP

“Moments form”

J ~ 1/U


Heavy Fermion Metals Review: cond-mat/0612006

UBe13


http://arxiv.org/abs/cond-mat/0612006


Heavy Fermion Metals Review: cond-mat/0612006

UBe13

Coherent Heavy Fermi Liquid





• Heavy electron Quantum Criticality:

Experiments


Pc P

AFMmetal

Heavy FermionMaterials

H. Von Lohneyson (1996)

Quantum Criticality: divergent specific heat capacity

Quantum CriticalPoint


Gegenwart et al (2002)T-Linear T-Linear

T2 T2

T2

Divergence ofInteraction and Effective Mass


“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”.


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


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

Jump in the Hall constant at a field tuned QCP.



Reconstruction of the Fermi Surfaceand mass divergence

Tuson Park, (2007).CeRhIn5



Shishido et al (2006)

Reconstruction of the Fermi Surfaceand mass divergence

Tuson Park, (2007).CeRhIn5




“Black hole in the phase diagram”


“Black Hole in the Phase Diagram”.

Zachary Fisk


Pc P

AFMmetal


Zachary Fisk


Pc P

AFMmetal

P.C and A. Schofield, Nature (2005)


Zachary Fisk


Pc P

AFMmetal



\ “PHASE

HORIZON”

Zachary Fisk


Pc P

AFMmetal


N


\ “PHASE

HORIZON”

Zachary Fisk


Pc P

AFMmetal



D

\ “PHASE

HORIZON”

Zachary Fisk


Pc P

AFMmetal


A


\ “PHASE

HORIZON”

Zachary Fisk


Pc P

AFMmetal

John Hertz: Critical droplet is Quantum if


A


\ “PHASE

HORIZON”

Zachary Fisk


Feynman Hertz


Feynman Hertz

Quantum Criticality: Casimir effect in time

QCP

Temperature NOT a tuning Parameter,

but a finite size effect in time.

(Hertz, PRB, 14, 1165 (1973).

Finite size

ωn = 2πkBT × n, ξτ =�

kBT


Feynman Hertz


QCP



(Hertz, PRB, 14, 1165 (1973).

Finite size


kBT

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


Pc P

AFMmetal

Feynman Hertz


QCP



(Hertz, PRB, 14, 1165 (1973).

Finite size


kBT



Pc P

AFMmetal

Feynman Hertz

Quantum CriticalBubble




Pc P

AFMmetal

Feynman Hertz





Pc P

AFMmetal

(Q) Quantum critical region:interior of correlation bubble.

Feynman Hertz

(Q)





Pc P

AFMmetal

(P) Paramagnet: probesexterior of correlation bubble

(Q) Quantum critical region:interior of correlation bubble.

Feynman Hertz

(Q)


(P)



E/T Scaling:

Meigan Aronson

M. C. Aronson et al, PRL 75, 725 (1995).


E/T Scaling:

Meigan Aronson


CeCu6-xAux (x=0.1)Schroeder et al, Nature407,351 (2000).

Almut Schroeder


E/T Scaling:

Physics Below the upperCritical Dimension.

Meigan Aronson


CeCu6-xAux (x=0.1)Schroeder et al, Nature407,351 (2000).

Almut Schroeder




Failure of the Standard model


Standard Model: Quantum SDW?

•Moriya, Doniach, Schrieffer (60s)•Hertz (76)•Millis (93)

F.S. instability

Fermi

Surface

HertzDoniach Schrieffer Millis Moriya




F.S. instability

Fermi

Surfacevertex non- singular





Time counts as z =2 scaling dimensions

F.S. instability

Fermi






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

Fermi




Singular potential is rapidly modulated:only affects electrons along hot-lines.

Predicts:

Landau’s Fermi Liquid ShouldSurvive at a Quantum Critical Point.



Q

Predicts:




Q

k-qk

q

Predicts:




Q

k-qk

q

divergent

Predicts:




Q

finite

k-qk

q

divergent

Predicts:



• 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.• New Ideas: breakup of the electron.


New Ideas


• Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode,Fluctuations critical in time.

Requires a two dimensional spin fluid

New Ideast

HSi, Ingersent




New Ideas

Schroeder et al, Nature 407,351(2000).

Locality of critical fluctuations

T.0.75(K0.75)

t

HSi, Ingersent


t

HNew Ideas Si, Ingersent




• Deconfined Criticality: Two diverging length-scales. (Hermele et al 2004; Senthil et al, Science 2004).

t

H

Critical Matter

Free spinons

Magnetic order

New Ideas

Senthil Sachdev Vishwanath

Si, Ingersent




• Deconfined Criticality: Two diverging length-scales. (Hermele et al 2004; Senthil et al, Science 2004).

t

HNew Ideas

Senthil Sachdev Vishwanath

Si, Ingersent




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


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


ψ(x, τ)

S[ψ]

τ, x

Wild quantum fluctuations!

New Ideas


Pepin


Large N limit

ψ(x, τ)

S[ψ]

τ, x

Wild quantum fluctuations!

New Ideas


Pepin


Large N limit

ψ(x, τ)

S[ψ]

τ, x

1N∼ �eff

New Ideas


Pepin


ψ(x, τ)

S[ψ]

τ, x

1N∼ �eff

Large N limit

New Ideas


Pepin


ψ(x, τ)

S[ψ]

τ, x

1N∼ �eff

classi

cal p

ath

Large N limit

New Ideas


Pepin

Electron

Spinon

Holon

Electron


ψ(x, τ)

S[ψ]

τ, x

1N∼ �eff

classi

cal p

ath

Large N limit

New Ideas


Pepin

Electron

Spinon

Holon

Electron

ZaanenM Cubrovic, J Zaanen, K Schalm - Science, 2009

Liu McGreevy


• 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.• Qu-frustration.


Qu- frustration• Frustration and Kondo have different effects.



AFM

K ~ TK/JH

Large FS Heavy Fermi Liquid



AFM

Q

Spin Liquid



AFM

Q

Spin Liquid


K ~ TK/JH



AFM

Q

Spin Liquid


K ~ TK/JH

metal


f~1/S

“Doniach” TK/JH

AFM

SLM


S. Nakatsuji et al, Nature Physics (2008).

!-YbAlB4

Experimental Support


f~1/S

“Doniach” TK/JH

AFM

SLM



!-YbAlB4


Non-Fermi liquid at B=0.Small field restores Fermi liquid behavior.


f~1/S

“Doniach” TK/JH

AFM

SLM



!-YbAlB4



Critical Phase?


f~1/S

“Doniach” TK/JH

AFM

SLM


?


!-YbAlB4



Critical Phase?

See:A. Nevidomskyy & PC PRL (2009).T. Senthil, S.Sachdev, M.Vojta,PRL 90,216403; PRB 69, 035111 (2004);P. W.Anderson, arXiv:0810.0279 (2008)


Q

K ~ TK/JH

AFM

SLM


Experimental Support II

Canfield et al (unpublished)


Conclusions.


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

Conclusions.



• Fermi surface expansion and the loss of AFM need not coincide.


Conclusions.




• Introduction of the “frustration” axis permits a unified treatment of spin liquid and Kondo effects.



Conclusions.







Spin Liquid

AFM

“Frustration”1/S


“Doniach” TK/JH

metalConclusions.





• Spin liquid Kondo states may have been observed in three Yb heavy electron systems. More experiments needed.




Spin Liquid

AFM



“Doniach” TK/JH

metalConclusions.










Spin Liquid

AFM



“Doniach” TK/JH

metalConclusions.


51

Collaborators

Rebecca Flint RutgersAndriy Nevidomskyy RutgersMaxim Dzero U. MarylandJerome Rech, CNRS, MarseilleEran Lebanon, Israel.Indranil Paul, CNRS, GrenobleLucia Palova RutgersPremi Chandra RutgersGergely Zarand BudapestOlivier Parcollet SpHT Paris.Andy Schofield BirminghamQimiao Si Rice, HoustonCatherine Pepin SpHT Paris.Almut Schroeder Kent StateGabriel Aeppli LCNHilbert v. Lohneysen Karlsruhe

37

Flint Nev. Dzero Rech Lebanon


qu-transitionscoleman/talks/kanpur_colloq2010... · 2013. 10. 8. · criticality - universal...

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