AC conductivity of a holographic strange metal

Transcription

1 AC conductivity of a holographic strange metal F. Peña-Benítez INFN - Perugia in collaboration with Elias Kiritsis Workshop on Holography and Condensed Matter 1

2 motivation holography is a good tool for the understanding of new states of matter strange metals seem to have a quantum critical point at zero temperature the scattering rate is only fixed by the inverse of T scaling tails in the frequency dependence [van der Marel et. al 2003] 2

3 motivation holography is a good tool for the understanding of new states of matter strange metals seem to have a quantum critical point at zero temperature the scattering rate is only fixed by the inverse of T scaling tails in the frequency dependence [van der Marel et. al 2003] 3

4 outline motivation a model for non fermi liquids results more general geometries outlooks 4

5 DC conductivity in translational invariance systems the DC conductivity is infinity = K (!)+ i +...! to have a finite DC conductivity translations must be broken in holography it is possible to have also finite conductivities using DBI systems in the probe approximation 5

6 the model (Massless) Fundamental matter in the probe limit on a background of adjoint matter quantized in light cone coordinates. Breaks relativistic invariance

7 the model AdS-Schwarzschild metric in light-cone coordinates ds 2 = g ++ (dx + ) 2 + g (dx ) 2 +2g + dx + dx + X g yy (dx i ) 2 + g uu (du) 2 DBI action (probe limit) L p det (g + F ) Light-cone electric field switched on A =(Ey + h + (u))dx + +(b 2 Ey + h (u))dx +(b 2 Ex + h y (u))dy 7 [E. Kiritsis et. al 2012]

8 DC conductivity computing DC conductivity using Karch O Bannon 2 = 2 0( 2 DR + 2 QC) scaling variables [E. Kiritsis et. al 2012] 8 t T E 1/2 J 2 2 E 3

9 DC conductivity computing DC conductivity using Karch O Bannon 2 = 2 0( 2 DR + 2 QC) 2 QC = t3 p A(t) 2 DR = J 2 t 2 A(t) A(t) =t 2 + p 1+t 4 scaling variables [E. Kiritsis et. al 2012] 9 t T E 1/2 J 2 2 E 3

10 parameter space q = 2 DR QC 10

11 now we switch on fluctuations for the gauge field on top of the previous background configuration

12 results (analytics) Schrödinger problem & optical conductivity linearized field equations 00 + V! 2 =0! T 1/3 e i /6 c 1 (r 0,T eff )+ic 2 (r 0,T eff )! 1 r 0! 1,! 1 12

13 results (numerics) Drude behavior pair creation = DC 1 i! drag regime

14 results (numerics) full optical conductivity t 3/2 blue red t magenta green 14

15 results (numerics) full optical conductivity t blue red t 2 magenta green 15

16 Summary I the DBI model has an UV power law with exponent -1/3 intermediate regime that can not be seen from analytics arguments in absence of charge density no Drude peak, only the UV power law appear the charged system shows a Drude peak 16

17 Einstein Maxwell dilaton model in order to have scaling geometries but violating hyper scaling and with Lifshitz exponent S Z p g apple R 1 2 (@ )2 + V ( ) Z 1 ( ) 4 F 2 1 Z 2 ( ) 4 F 2 2 ds 2 = r 2 d apple dt 2 r 2z + dr2 + dx 2 r 2 Z 1 Z 2 Z 2 =0 Z 2 >Z 1

18 conductivity for uncharged gauge field Z 2 =0! m m = 3 2 z + d z 1

19 conductivity for uncharged gauge field conductivity for charged gauge field! m 1! m 2 19

20 Summary II to have negative exponent in EMD systems it is necessary at least two gauge fields full AC conductivity with the full RG flow geometry has to be computed are the scaling tales completely determined by the pair creation physics in general systems? 20