Transcript Exploring New Paradigm

Exploring New Paradigm
in Physics
Yu Lu
Institute of Physics
Chinese Academy of Sciences
“…The underlying physical laws
necessary for the mathematical theory of a large part
of physics and the whole of
chemistry are thus completely
known, and the difficulty is
only that the exact application
of these laws leads to equations much too complicated to
be soluble.”
P.A.M. Dirac, Proc. Roy. Soc. A123, 713 (1929)
How do you do to get the Theory of
Everything?
1. Planck/unification scale
(1028 eV)
2. QCD  Nuclear physics scale
(108-109 eV)
d
u
u
du
d
e
d u
u
+ 2e
4 He
u
d d
e
3. Condensed matter physics scale
(100 eV)
+
+
+
+
+
+
+
+
+
+
+
+
-
Na metal
The Theory of Everyday Everything!
Great achievements of quantum
theory and relativity:
Civilization of the information Age
 Structure of matter: how chemistry ‘works’
 Electronic theory: transistors, IC, memories
 Lasing principle: lasers, optical fibers…
 Fission and fusion: nuclear energy…
 Nuclear Techniques: MRI, PET, CT…
Observations and exploitations of these
remarkable quantum phenomena
Is this truly The theory of
Everything?
Can one derive ALL exotic properties,
from the Schrödinger equation??
“We often think that when we have
completed our study of one we know
all about two, because ‘two’ is ‘one
and one.’ We forget that we have
still to make a study of ‘and.’ ”
--Sir Arthur Eddington.
Philip W. Anderson:
More is different (1972)
“The behavior of large and complex aggregations
of elementary particles, … is not to be
understood in terms of a simple extrapolation of
the properties of a few particles. Instead, at
each new level of complexity, entirely new
properties appear, and the understanding of this
behavior requires research as fundamental in its
nature as any other…”
Emergent features of
condensed matter systems




Collective excitations—quasi-particles
Symmetry breaking
Renormalization
……
Lattice vibration and phonons
 If ground state stable: low energy excitations
—harmonic oscillations. Quantization of these
oscillations — phonons
 “Like” ordinary particles，dispersion  (p)
 No restrictions on generation: bosons
 They cease to exist, while away from crystals:
quasi-particles
 Not sensitive to microscopic details，those
details cannot be recovered from the phonons
This was initiated by Einstein ！
Landau Fermi Liquid Theory
 Low energy excitations of interacting Fermi
systems（like electrons in metals）can be
mapped onto weakly interacting Fermi gas
 These quasi-pariticles follow Fermi statistics，
with dispersion  (p)，with the same Fermi
volume as free fermions (Luttinger theorem).
 They cease to exist if taken away
matrix (metal)
from the
 Their properties not sensitive to microscopic
interactions，which cannot be derived from
these ‘coarse grained’ properties
Basic assumption:
Adiabaticity
Question: How to justify it, if
no gaps?
Emergent features of
condensed matter systems
 Collective excitations—quasi-particles
 Symmetry breaking
 Renormalization
……
Superconductivity
1911 Kamerlingh Onnes
discovered zero resistance
Early 30s Meissner effect
discovered, complete diamagnetism more fundamental
London equations
2
d Js
c2
m
*
c
2
Js 
A
,

E
,

L 
2
2
4L
dt 4L
4ns e *2
c
Wave function “rigidity” ansatz (London brothers)
ne
e
J
( 0 | P | 0   A)
m
c
Superconductivity
1950 Ginzburg-Landau equation，introducing
macroscopic wave function
i
  e
1
2e 2
(i 
A)   a(T  Tc )   |  |2   0
4m
c
ie
2e 2
J s (r )  
( *   *) 
|  |2 A
2m
mc
Bardeen realized: gap in spectrum leads to “rigidity”
Cooper pairing：arbitrarily weak attraction gives
rise to bound states at the Fermi surface
—pairing energy is the gap
Is SC a Bose-Einstein condensation of
Cooper pairs?--a bit more complicated!
BCS wave function：
   (uk  vk ak ak  ) | 0; uk2  vk2  1
k
Problem solved！
Nobel prize was delayed by 15 years！!
Particle number not conserved，change from one
Hilbert space to another one — symmetry
breaking—conceptual breakthrough
Symmetry Breaking
Discrete symmetry－－from up
or down to definite up（down）
Broken symmetry－reduction of symmetry elements
Displacive phase
transition
“Usually”:
symmetry”,
“high temperature－high
“low temperature－low symmetry”
Broken continuous symmetry
Ferromagnet--broken
rotational symmetry
Antiferromagnetic order – staggered magnetization
(Landau & Néel)， －－not conserved quantity
Macroscopic superconducting wave function
－ order parameter (Landau)
i
  e breaking of U(1) gauge symmetry
Anderson-Higgs
mechanism
Goldstone mode: collective excitations,
recovering the symmetry – like spin waves
When external (gauge) field coupled, becomes
massive -- Meissner effect
Unified weak-electromagnetic interactions－
1979 Nobel prize in physics
Weinberg- Salam- Glashow
Josephson effect：
visualization of the phase
J  J 0 sin(1   2 );
2e
 2eV0
J  J 0 sin(0  V0t ),


t

Using two Josephson junctions-- SQUID
I max  2I c cos(2 / 0 ), 0  hc / 2e
Most profound exhibition of emergence!
Josephson Effect
S2
S1
e1
e
i 2
e
i1
Bardeen - Josephson dispute
 Anderson’s lecture
 Josephson’s calculation
 Bardeen’s added note
 Dispute at LT 8
BCS mentor against
the most convincing
proof of his theory!!
Quark-Gluon Plasma
Neutron Stars, Color Superconductivity
High Tc Superconductivity
Low Tc Superconductivity
Heavy Electron Superconductivity
3He
Superfluidity
Atom traps, BEC, Superfluidity
10-9
10-6
10-3
Nano-K micro-K milli-K
1
K
103
kilo-K
106
109
1012
mega-K giga-K tera-K
Emergent features of
condensed matter systems
 Collective excitations—quasi-particles
 Symmetry breaking
 Renormalization
……
Failure of Mean Field Theory！！
MFT
a

g
d
n

Experiment
0 (jump）
1/2
1
3
1/2
0
0
 1/3 !
 4/3 !
5 !
 2/3 !
0
Theory valid in space dimensions beyond 4 ！
Renormalization Group (RG) Theory of
Critical Phenomena -- 1982 Physics Nobel
Kenneth K. Wilson
Basic Ideas: First integrate out
short range fluctuations to find
out how coupling constant
changes with scale. Using
expansion around “ fixed ” point
to calculate the critical
exponents, in full agreement
with experiments, without any
adjustable parameters.
Experimental verification of RG theory
Newest results of RG
a=-0.0110.004
Space experiment
(7 decades)
a=-0.01270.0003
Full agreement within
accuracy
Power of Theoretical Physics !!
Justification of Landau Fermi
-liquid theory
—Weakly interacting fermion
systems renormalize to its ‘fixed
Point’—Free fermions
Paradigm in studying
Emergent phenomena
 Low energy excitations: quasi particles
 Landau Fermi liquid theory
 Symmetry breaking
 Renormalization
 …….
Very successful, common features of
phenomena at very different scales,
but is it a universal recipe??
Integer Quantum Hall Effect
－ 1985 Nobel in Physics
No symmetry breaking
Failure of Landau
paradigm !!
X.G. Wen
Topological properties of QHE
e2/h=1/(25 812.807 572 Ω) accuracy 10－9
N=n Chern number
QHE and Quantum Spin Hall Effect
Qi & Zhang
Topological insulators
Bulk-insulator, surface-metallic, no timereversal symmetry breaking, no backscattering, guaranteed by topological
Chern parity!!
Plausible exotic excitations
Charge+monopole-‘Dyon’ Majorana fermion
Axion?
X.L. Qi et al.
No answer yet to the challenge
Posed by Müller-Bednorz!!
LSCO –La2-xSrxCuO4+d
YBCO -- YBa2Cu3O6+y
Not so much the Tc so high,
super-glue?
Even more profound problem:
the Fermi liquid theory fails!
“Anomalous” normal state properties
mysterious linear resistivity
H. Takagi et al.
PRL, 1992
Pseudogap of High-Tc
(dark entropy)
Missing of entropy at
low energies
600
(c)
0.97
0.92
0.87
0.80
0.76
0.73
0.67
0.57
0.48
0.43
500
400
300
200
0.38
0.29
0.16
100
0
0
50
Concept of quasiParticle not applicable
100
150
T(K)
200
250
300
Attempts to explore new paradigm
 Topology + quantum geometry
(D. Haldane)
 Topology + long range entanglements
(X.G. Wen)
Laughlin’s wave function for FQHE
Fractional charge, fractional statistics,
……
Is this a complete description??
New question raised by Haldane
Are these two ‘circles’ the same?
Using geometrical approach they are not
the same!!
The latter is described by the “guiding
centers” which obey ‘non-commutative
geometry’!!
How to characterize topological order?
 No symmetry breaking, nor local order
parameter, different quantum Hall
states have the same symmetry
 Non-local topological order parameter
 Ground state degeneracy-Berry phase
 Abelian-Non-Abelian edge states (CFT)
 Gapped spin-liquid states, protected by
symmetry, chiral spin state, ……
What is the most fundamental??
X.G. Wen
Quantum Entanglement
EPR paradox
Classical orders (crystals, ferromagnets)-untangled
Even the ‘quantum order’-superfluidity-untangled
Classification of entanglements
 Short range entanglement
• Landau symmetry breaking states
• No symmetry breaking- Symmetry protected
topological order like topological insulators,
Haldane spin 1 chain……
 Long range entanglement
•Symmetry breaking like P+iP superconductivity
•No symmetry breaking: FQHE, spin liquids
Non-trivial topological order
= long range entanglement in MB states
Some key words
 Topology
 Geometry (non-commutative)
 Long-range entanglements
 Entanglement spectrum, instead of
just a number (von Neumann entropy)
……
Thank you all!