1. On magnetization in holographic models
International Workshop for String Theory and Cosmology (STCOS 2015)
June 29 (Mon), 2015 ~ July 01 (Wed), 2015
Kyung Kiu Kim(GIST)
with
San-Jin Sin(Hanyang Univ.), Yunseok Seo(Hanyang Univ.)
and Keun-Young Kim (GIST)

2. Motivation AdS/CMT Ferromagnetism High Tc superconductors
Anti-ferromagnetism
Meissner Effect
Nernst Effect, Hall angle, ….

3. Contents
Why is magnetization important in AdS/CMT ? -Ferromagnetism -High Tc superconductor phase diagram ▷Superconducting phase 》 Holographic superconductor with Meissner effect ▷Normal phase of superconductor 》 Magnetic property (Nernst Effect, Hall angle) ▷Insulator phase of superconductor 》 Anti-ferromagnetism (Mott Insulator) -Magnetic Impurity ▷ Anomalous Hall effect, Magneto resistance, …
Holographic models to describe these physics - Magnetic impurity model in more detail - Real scalar spontaneous magnetization model in more detail
Summary

4. Ferromagnetism An applied magnetic field classifies materials.
Also, turning off the magnetic field

5. Ferromagnetism Magnetization without External magnetic field
< M > ≠ 0 with B = 0

6. Ferromagnetism
Hysteresis Curve

7. Ferromagnetism
Phase transition can be descried by the Landau-Ginzburg model with a real scalar.
The model is given by

8. Phase transition with an effective model

9. A comment on 2+1 dimension
In the real condensed matter:
2+1 dimension is not 2+1 dimension ▶ 2+1 dimensional material with 3+1 dimensional theory
Introduced in Cai and Sin’s talk
In 2+1 dimension L_{12} is like a helicity in 3+1 dim…

10. High Tc superconductor
Demilitarized zone(DMZ) of phase diagram
Magnetic mines are spread all over the phase diagram

11. A digression
Typical properties of superconductor -Fundamental property : Meissner effect -Subsidiariness : Infinite conductivity
Orignal holographic superconductor has a problem.
Normal state : RN black hole Superconducting state : Hairy black hole
Holographic DC conductivity - RN black hole(Infinite conductivity) from translational invariance - Hairy BH(Infinite conductivity) from translational invariance + superfluid density

12. Recent development : breaking translational invariance by
Explicit space coordinate dependence -Explicit Lattice : PDE problem -> Horowitz, Santos and Tong(2012) -Massive gravity : Breaking diffeomorphism by mass term of graviton (ODE) -> Vegh(2013) -Axion model : Linear massless scalar to avoid PDE (ODE) -> Andrade and Withers(2013) -Q-Lattice model : more general model than the Axion model (ODE) -> Donos and Gauntlett(2014)

13. Holographic superconductors in every version -Explicit Lattice : Horowitz and Santos(2013) -Massive gravity : Cheng and Wu(2014) -Q-Lattice : Liu, Niu, Wu and Xian(2014) -Axion Model : Andrade and Gentle(2014) Kim, Kim and Park(2015)
Typical AC conductivity

14. Meissner Effect of Holographic superconductor(Hartnoll, Herzog and Horowitz 2018) : We need Magnetization for strict Meissner effect

15. Normal phase of the superconductor
Strange Metal
Nernst Signal

16. Nernst signal becomes stronger as the paramaters(Tem perature, Dopping) goes to Quantum Critical Point
Special shape of Signal to magnetic field by vortex fluid

17. Anti-ferromagnetism region in high Tc SC
-> Cai’s talk

18. Magnetic Impurity -Anomalous Hall effect -Magneto resistance -Magneto electric effect -…

19. Holographic model of magnetic Impurities
When = 0
The Axion field plays a role of impurity (Kim, Kim, Seo and Sin (2014))

20. Why ?
Back to a model without impurity
Background solution is Dyonic BH(Hartnoll Kovtun Muller and Sachdev 2007)
Thermodynamic potential is the on-shell action by AdS/CFT dic. .
The magnetization is defined as

21. Considering a fluctuation solution
One can compute
This is not ferromagnetic material because B=0 -> M =0
If there is a term
There is a possibility for the spontaneous magnetization M without B

22. Possible terms
Cai’s approach and Sin’s approach in their talks - M tensor is proportional to a polarization tensor.
-Magnetization is proportional to the charge density because F_{rt} is the charge density by AdS/CFT dic..
Dual theory is like a Chen-Simon matter theory.

23. Without -> A model with impurities
With -> A model with magnetic impurities
Exact solution

24. Charge density
Magnetization
Energy
Thermodynamic stability is guaranteed for small

25. Magnetization

26. Also, this solution is an exact solution of a massive gravity.

27. The DC conductivity

28. An interesting magneto-resistance

29. Spontaneous magnetization model
In our computation we took n=2. We are calculating for other cases.
Without
This is same with a holographic superconductor model with a real scalar. -> Spontaneous Z_2 symmetry breaking

30. Without
There is a transition from RN BH to a hairy BH which is dual to a phase transition related to real order parameter.
This operator expectation value has nothing to do with magnetization.

31. With
Solve background and fluctuation numerically.
We obtained a spontaneous magnetization using real scalar condensation.

32. Summary Magnetization is important in condensed matter physics.
AdS/CMT has to reproduce phenomena related to magnetization.
We constructed a magnetic impurity model and a spontaneous magnetization model.

33. Thank you very much !