Holographic spin fluctuation and Competing order. Sang-Jin Sin Florence

Transcription

1 Holographic spin fluctuation and Competing order Sang-Jin Sin Florence

2 General comment: ads/cmt Try to get scaling exponents mean field theory value (due to analyticity). continuum theory: Details inside a cell are averaged out. Not a tool for seeking micropic pairing mechanism. In gravity limit, AdS/CFT is a mean field theory

3 A Goal OF AdS/CMT quantitative understanding the phase diagram NFL FL Based on Royal Society publishing, D. Galanakis et.al 3

4 To classify phases / To set up MFT we need order parameter although here Order is by interaction not by symmetry. Finite number of Phases finite number of order parameters (fields). For Pseudo Gap region : Not clear what kind of order. Scalar? Vector? or something else?

5 Order parameter. We need order parameter although it is NOT completely controlled by symmetry. What is the hint to characterize the order parameter of theoretically unknown region? If we have general results on the competition/collaboration of order parameters in general, it can give a guide.

6 Only two regions clear AFM: real scalar; SC: complex scalar NFL FL Spin fluc. / Charge fluc. 6

7 Competing order in holography Conjecture (Basu et.al ) Repulsive/attractive int. orders coexist/repel Ex1. Ex2. Holography without potential. SC : complex scalar, pick some order : Real scalar If they attract simply by gravity Two orders repel each other. (corollary of conj.) Holography confirms!

8 Q: How about SC v.s vector order? by Takaaki Ishii and SJS

9 er a holographic superconductor where an extra massive vector field is introd ies. model section 5. section 5. 2 Impuritydegrees of of freedom freedom by by a massive a massive vector vector field field Complex scalar+ extra vector We consider a holographicsuperconductor wherean wherean extra extra massive massive vector vector field field isintroduced as impurities er a model where a massive vector field is introduced into the minimal Abe 2.1 T he model el of the s-wave holographic superconductor [12]. T he action is 2 We consider a model where a a massive vector vector field field is is introduced into into the minimal the minimal Abelian- Higgs model of of the the s-wave holographic superconductor [12]. [12]. The The action action is 2 is 2 S = d 4 x g 1 4 F µνf µν µ Φ ia µ Φ 2 M 2 Φ 2 S = d 4 x S = d g 1 4 x g 4 F 1 µνf µν µ Φ ia µ Φ 2 M 2 Φ 2 4 F µνf µν µ Φ ia µ Φ 2 M 2 Φ G µνg µν m2 2 B µb µ c 1 2 F µνg µν, 4 G µνg µν m2 1 4 G µνg µν m2 2 B µb µ c 2 F µνg µν, (2.1) 2 B µb µ c 2 F µνg µν, where F = da and G = db. The scalar field Φ is charged only under A µ,and there is da and G where = db F =. da The andscalar G = db field. TheΦscalar is charged field only under A µ no direct coupling between Φ and B µ coupling between Φ and B µ. Here m 2. Here m 2 Φ is charged only under A µ,and the is the mass of B µ. It might be possible no direct coupling between Φ and B to consider to generate this mass by some µ is. Here them Higgs mass mechanism, 2 is the of mass B µ. of It B but here µ. might It might be be pos we would like to rthe to other, to generate st B consider to generate this mass by some Higgs mechanism, but here we artthis from the mass Proca byaction some for simplicity. Higgs mechanism, The scalar massbut ischosen here to we be Mwould 2 would lik µ, represents impurities. (in If v2) we or spin allow current the (in difference v1) in = 2for lik convenience st art from the in analysis. Proca action for simplicity. The scalar mass ischosen to be M 2 the Proca action Theaction for (2.1) simplicity. has an interaction T he scalar term between massf ischosen to be M 2 = s of the Title two current operators, the vector field dual to the impurities convenience in analysis. µν and G µν.these vector fields = are ssociated e in analysis. v1: A with ferromagnetic dual the The to two action Proca currentswith (2.1) field. superconductor has different an interaction dimensionality, term in holography between and thisinteraction F µν and G µν representsa.these vector coupling field of dual theto two two currentswith [17]. One different current dimensionality, is conserved fermion and thisinteraction number, and representsa A ction it in which v2: (2.1) Impurity has the an matter interaction effect fields a doholographic term not give between back-reactions superconductor F µν G the µν.these backlimit vector µ is identified coup field as of the gauge two currents field of [17]. the weakly-gauged One current is U(1) conserved electromagnetic fermion symmetry number, and in the A µ context is ident currentswith is called a different probe limit. dimensionality, The gravity and background this interaction we consider represents is a coup

10 Results In the presence of SC condensation of CS, vector condensation (Bt) is actually induced by it coexists. The sign of Bt condensation is that of coupling c G.F As c goes up, SC gap goes like power rather than exponential. Without SC, no vector condensation in Bt. (sign of c is immaterial for the existence of <Bt>)

11 Result: ac conductivity Figur e 5. Comparisons of the real part of the conductivity for c = 0 (orange dotted lines) and c =0.2, 0.3, 0.4, 0.5 (blue real lines) computed when T/T C =0.20. T he left panel is when = 1, and the right panel is when = 2. Exponential and power-law behaviors are interpolated by changing c. It is expected that the effects of the coupling turn up gradually as the coupling is increased from c = 0. To discuss this, we compare cases of different c. We compute the conduct ivity for c = 0.2, 0.3, 0.4, 0.5, by fixing m 2 for simplicity. We have to be careful

12 Result: coexistence of sc & vec Overlapping phase diagram Figur e 6. A schematic description of the phase diagram expected. Here B = 0 if c = 0, while B 0once c 0andT<T C. Gapped and ungapped phases would be interpolated smoothly. T here may be some critical c = c above which there is no mass gap. Figure 5 corresponds to looking at a horizontal slice of this diagram at T/T C =0.20. and thus the effects might be harder to appear.

13 Result (spin susceptibility / impurity conductivity)

14 Implication to PG order parameter. If the PG phase is a phase of incoherent paired state(precursor of SC), we should use the vector order parameter for PS. Not a scalar! (Scalar with negative potential is also OK). We need to introduce two scales: One for SC and the other for PS which is of order T*. If PG itself is an order competing with SC, its order parameter can be a real scalar. Possibly with attractive interaction. If PG is a spin Liquid: Not in this talk. (Top.O)

15 magnetism with axion Motivation. We want to control the magnetism by changing the dopping parameter. Spin is not totally independent of charge. So we use the Chern-Simon / Axion term.

16 with Yunseok Seo ^, ^ Hanyang univ. Keun-Young Kim*, Kyung-Kyu Kim* *GwangJu Institute of Science and technology References: (Iqbal et.al); Basu et.al 16

17 Action

18 Solution In terms of the horizon radius r0,

19 Thermodynamics

20 Magnetization

21 B dependence of M

22 Q: What about the antiferromagnetic spin fluctuation? Introduce a scalar field as a spin wave order parameter. With the same philosophy as before, introduce CS coupling : * scalar represent angular fluctuation in non-linear sigma model.

23 result

24 Interpretation Condensation of real scalar: new order is set by coupling it to F^F term. This is not by a symmetry breaking. The gap was induced by dynamics. This may be a new order. May be Relevant to

25 Story2 +Story3 Chi is the master field of Magnetization x,y dependent part is the non-normalizable source term. x,y independent part is the magnetic charge/b-field term and is described by phi term is its fluctuation.

26 Conclusion Interaction between the order parameters are very useful guidelines to set up a model. In the presence of coupling to F^F Momentum dissipating impurity induces a permanent magnetization. In the presence of coupling to F^F, real scalar Neither are not related to symmetry breaking.