Post on 22-Aug-2020
transcript
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r↵ ⇥A = BZ
B · darea 6=I
A · d`
�xx
/ T (d+2��2)/z
↵xx
/ T (d+��2)/z
xx
/ T (d+z�2)/z
�xy
/ BT (d+3��4)/z
xy
/ BT (d+z+��4)/z
↵ = 1 + 2/3 = 5/3
:
Philip W. Phillips and Kridsanaphong Limtragool (arxiv.org/1601.02340)
Strange Metal
Experimental Detection of the Anomalous Dimension of the Current in the Strange Metal from the Fractional Aharonov-Bohm Effect
�(!) = C!� 23
n⌧e2
m
1
1� i!⌧
T-linear resistivity
Lxy
= xy
/T�xy
6= # / T
1
�2/3
single-parameter scaling
⇢ / T (2�d)/z
�(!, T ) / !(d�2)/z
Cv / T d/z
⇠⌧ / ⇠z
does not work
solution
fractionalnot d-1
[J ] = �
What does interwined order have todo with the Strange Metal?
So lets focus on the Strange Metal?
why an anomalous dimension?
ac transportLimtragool/PWP
dc transportKarch/Hartnoll
�i(!) =nie2i ⌧imi
1
1� i!⌧i
�(!) =
MZ
0
⇢(m)e2(m)⌧(m)
m
1
1� i!⌧(m)dm
continuous mass d�(m) = �(m)dm
a+ 2b� 1
c= �1
3
�(!) =⇢0e
20⌧
130
M
1
!
23
!⌧0Z
0
dx
x
� 13
1� ix
!⌧0 ! 1
�(!) =1
3(p3 + 3i)⇡
⇢0e20⌧130
M!23
tan� =p3
60�
momentum loss
anomalous dimension
hyperscaling violation⇢(m) = ⇢0
ma�1
Ma
e(m) = e0mb
M b
⌧(m) = ⌧0mc
M c
the Lorenz ratio is not a constant
LH =xy
T�xy⇠ T ⌘ T�2�/z
� = bz = �2/3choose solution
Experiment: Probe scaling dimensionof vector field
how can an anomalous dimension be detected
independent of any
Aharonov- Bohm
flux
�� =e
~
I~A · d`
�� =eB⇡r2
~
what if B has an anomalous [B] = L�2↵ ↵ 6= 1
�� =eB⇡r2
~
is no longer
�� =eB⇡r2
~ F (L,↵)
non-locality of the
solution
gauge invariance field strength
ai ⌘ [@i, I↵i Ai] = @iI
↵i Ai
aµ ! aµ + @µ⇤
� ~22m
(@i � ie
~ai)2 = i~@t .
Fµ⌫ = 2@[µA⌫],Aµ ! Aµ + @µG
~r↵ · ~J + @t⇢ = 0 continuity eq.
F↵µ⌫ = @↵µ
µ A⌫ � @↵⌫⌫ AµAµ ! Aµ + @↵
µG
proof
compute AB phase�� =
e
~
I~a(r0) · ~d`0
use fractional calculus
��R =eB`2
~
✓b↵�1d↵�1
�2(↵)
◆c � l, d � l
AB phase has to change
��D =e
~⇡r2BR2↵�2
p⇡21�↵�(2� ↵)�(1� ↵
2 )
�(↵)�( 32 � ↵2 )
sin2⇡↵
22F1(1� ↵, 2� ↵; 2;
r2
R2)
!
is the correction large?
yes!
��D =eB`2
~ L5/3/�(5/3)2
combine AC+DC
fixes all exponentsa,b,c
[J ] = dU
probe withAharonov-Bohm effect
b 6= 0
Monday, February 1, 16