?

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