Recent Advances in Holographic Magnetism from General Relativity

1. Hot Topics in General Relativity and Gravitation, Aug. 9-15, Quy Nhon, Vietnam HolographicMagnetism from GeneralRelativity Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences Refs: arXiv:1404.2856, PRD90(2014)081901 arXiv:1404.7737,PRD91(2015)086001 arXiv:1410.5080,PRD91(2015)026001 arXiv:1501.04481; arXiv:1504.00855,PRD92(2015)046001 arXiv:1505. 03405,(PRDinpress); arXiv:1507.00546;arXiv:1507.03105

2. Outline: 1Introduction 2Ferromagnetism/paramagnetismphase transition 3Antiferromagnetism/paramagnetismphasetransition 4Antiferromagnetic quantum phase transition 5Insulator/metalphasetransitionandcolossal magnetoresistanceeffect 6Coexistenceandcompetitionbetweenferromagnetism andsuperconductivity 7Summary

3. AdS/CFT correspondence（1997, J.Maldacena）: CFT AdS “Real conceptual change in our thinking about Gravity.” (E.Witten, Science285(1999)512

4. howtobuildaholographic model of superconductors CFT CFT/AdS Gravity Global symmetry Abelian gauge field Scalar operator Scalar field Temperature Black hole Phase transition High T/no hair Low T/ hairy BH G.T. Horowitz, 1002.1722

5. Holographic superconductors Building a holographic superconductor S. Hartnoll, C.P. Herzog and G. Horowitz, arXiv: 0803.3295 PRL 101, 031601 (2008) High Temperature（black hole without hair):

6. arXiv:1003.0010,PRD82 (2010) 045002 Breaking a globalSU(2) symmetryrepresenting spin into a U(1) subgroup. The symmetry breaking is triggered by condensation of a triplet scalarfield . This model leads to the spatial rotational symmetry breakingspontaneously, the time reversal symmetry is not brokenspontaneously in the magneticordered phase.

7. 2、A Model for ferromagnetism/paramagnetismtransition arXiv:1404.2856,PRD90(2014)081901,Rapid Comm. The Model:

8. We are considering the probe limit, the background is Temperature: Theansatz:

9. Theboundarycondition:

10. Theoff-shellfreeenergy: arXiv:1507.00546 onshell:

11. Spontaneousmagnetization:B=0

12. Theresponsetoexternalmagneticfield ObeytheCurie-WeissLaw

13. Thehysteresisloopinasinglemagneticdomain: When T < Tc, the magnetic moment is not single valued. Theparts DE and BA are stable, which can be realized inthe external field. The part CF is unstable which cannotexist in the realistic system. The parts EF and CB aremetastable states, which may exist in some intermediateprocesses and can be observed in experiment. Whenthe external fieldcontinuouslychanges, the metastable states of magneticmoment can appear.

14. 3、Faramagnetism/antiferromagnetismphasetransition arXiv:1404.7737 Antiferromagnetic material does not show any macroscopic magnetic momentwhen external magnetic field is absent, it is still a kind of magnetic ordered materialwhentemperature is below the Neel temperature T_N. The conventional picture, due to L. Neel, represents a macroscopic antiferromagnetism as consisting of two sublattices, such that spins on one sublattice point opposite to that of the other sublattice. The order parameter is the staggered magnetization, as the diference between the two magnetic moments associated with the two sublattices:

15. Magneticsusceptibility:

16. Threeminimalrequirementstorealizetheholographicmodel • forthephasetransitionofparamagnetism/antiferromagnetism. • TheantiparallelmagneticstructureasT<T_N • Thesusceptibilitybehavior • Breakingthetimereversalsymm&spatialrotatingsymm Ourmodel:

17. The probe limit Theansatz: Define:

18. Theequationsofmotion: Theboundaryconditions:

19. Theparameterconstraint: Theon-shellfreeenergy:

20. alpha_0andbeta_0areinitialvaluesatthehorizon!

22. Theinfluenceonstrongexternalmagneticfield

23. arXiv:1504.00855 Newmodel:

26. 4、Antiferromagneticquantumphasetransition

28. Linearresponsetheory: ifthespectrumfunctionhasapoleat

31. Neither power-law nor square root, but it is expected in strong coupling case. Indeed in the case d=z=2, the quantum critical theory is not in general a weak coupling theory. arXiv:1505.03405

32. 5、Insulator/metalphasetransitionandcolossal magnetoresistanceinholographicmassivegravity Somemagneticmaterialssuchasmanganites exhibitthecolossalmagnetoresistanceeffect. Ourmodel: Blake, Tong and Vegh, arXiv:1310.3832 BlakeandTong,arXiv:1308.4970 MeffordandHorowitz,arXiv:1406.4188 Thereisapositiondependentmass Thismeasuresthestrengthofinhomogeneity

33. Theblackbranesolution: Theansatz: Theasymptoticsolutionattheboundary:

34. DCconductivity: Theperturbation: TheAdSboundary: DCresistivity:

35. Bythemembraneparadigm: IqbalandLiu,arXiv:0809.3808 TheDCresistivityinthestronginhomogeneitylimit:

36. Numericalresults: A.Urushibaraetal,PRB51(1995)

37. 6、Coexistencebetweenferromagnetismand p-waveorder (arXiv:1410.5080) P-wave:Einstein-Maxwell-Complexvector model: arXiv:1309.4877,JHEP1401(2014)032

39. Ourmodel:

40. Theprobelimit: Theansatz: Itisfoundthatonlythefollowingcaseisconsistent

41. Define:

42. 1)Superconductingferromagnet

46. 2)Ferromagneticsuperconductor

49. Conclusions: 1)In thecase that the ferromagnetic phase appears first, if the interaction is attractive, thesystem shows the ferromagnetism and superconductivity can coexist in low temperatures. If the interaction is repulsive, the system will only be in a pure ferromagneticstate. 2)In the case that the superconducting phase appears first, the attractive interaction will leads to a magnetic p-wave superconducting phase in low temperatures.If theinteraction is repulsive, the system will be in a pure p-wave superconductingphase or ferromagnetic phase when the temperature is lowered.

50. 7、Summary • 1)Presentaholographicmodelfortheparamagnetism • -ferromagnetismphasetransition • 2)Theparamagnetism-antiferromagnetismtransition • Antiferromagneticquantumphasetransition • 4）Insulator/metalphasetransitionand • colossalmagnetoresistanceeffect • 5)Coexistenceandcompetitionbetweenferromagnetism • andp-wavesuperconductivity