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## Holographic quantum criticality from multi-trace deformations

Citations: | 26 - 3 self |

### Citations

345 | Lectures on holographic methods for condensed matter physics,
- Hartnoll
- 2009
(Show Context)
Citation Context ...Complete AdS4 expansion and boundary terms 51 1 Introduction Over the past couple of years, gauge/gravity duality has been applied to a number of problems in condensed matter physics (for reviews see =-=[1, 2, 3]-=-). An important feature of some condensed matter systems is the existence of quantum critical points, marking continuous phase transitions at zero temperature. One goal of the present work is to intro... |

274 | Breaking an Abelian gauge symmetry near a black hole horizon,”
- Gubser
- 2008
(Show Context)
Citation Context ...erature and causes a condensate to form. Previous constructions have started with a charged anti de Sitter (AdS) black hole which has such an instability when coupled, e.g., to a charged scalar field =-=[4, 5, 6]-=-. We will show that there is another source of instability which applies even for Schwarzschild AdS black holes. So these new superconductors can exist even at zero chemical potential and no net charg... |

200 |
Positive energy in anti-de sitter backgrounds and gauged extended supergravity.
- Breitenlohner, Freedman
- 1982
(Show Context)
Citation Context ...ion, the scalar field has an effective mass meff which depends on the original mass m and charge q of the scalar field. When this effective mass squared is below the Breitenlohner-Freedman (BF) bound =-=[14]-=- for AdS2, this near horizon region becomes unstable. Since m2 is above the BF bound of the asymptotic AdS4 geometry, the asymptotic region is stable, and the solution settles down to a black hole wit... |

196 |
AdS/CFT correspondence and symmetry breaking,
- Klebanov, Witten
- 1999
(Show Context)
Citation Context ... scalar field. The boundary conditions may be modified due to the addition of a multi-trace deformation in the dual field theory [15, 16], or simply due to alternative quantization of the bulk theory =-=[17]-=-. It was widely believed that if one added a double trace term with κ < 0, then the theory would not have a stable ground state. However, we have recently shown that this is not necessarily the case [... |

170 |
Gravity Duals of Lifshitz-like Fixed
- Kachru, Liu, et al.
(Show Context)
Citation Context ... critical solution with something else. This is exactly what happens when one studies the back reaction of fermions in the bulk [62], where the IR AdS2 ×R2 solution is replaced by a Lifshitz geometry =-=[63]-=- with a dynamical critical exponent zG ∼ O(1/GN) (we use a subscript G to denote a geometric exponent, to be contrasted with our z.) For zG →∞ one recovers the AdS2×R2 geometry. So finite zG is playin... |

164 |
Holographic superconductors,”
- Hartnoll, Herzog, et al.
- 2008
(Show Context)
Citation Context ...erature and causes a condensate to form. Previous constructions have started with a charged anti de Sitter (AdS) black hole which has such an instability when coupled, e.g., to a charged scalar field =-=[4, 5, 6]-=-. We will show that there is another source of instability which applies even for Schwarzschild AdS black holes. So these new superconductors can exist even at zero chemical potential and no net charg... |

150 | Holographic duality with a view toward many-body physics, Adv. High Energy Phys.
- McGreevy
- 2010
(Show Context)
Citation Context ...Complete AdS4 expansion and boundary terms 51 1 Introduction Over the past couple of years, gauge/gravity duality has been applied to a number of problems in condensed matter physics (for reviews see =-=[1, 2, 3]-=-). An important feature of some condensed matter systems is the existence of quantum critical points, marking continuous phase transitions at zero temperature. One goal of the present work is to intro... |

146 |
Effective holographic theories for low-temperature condensed matter systems,”
- Charmousis, Gouteraux, et al.
- 2010
(Show Context)
Citation Context ...eld σ which couples to the gauge field, considered first in the AdS/CMT context in [64].19 We will consider this model here as a concrete example. In our action (2.1) one replaces F 2 → e2ασF 2 19See =-=[43]-=- for further generalizations. 42 and adds a kinetic term for σ with normalization −2(∇σ)2 . We will not add a potential for σ. There are many choices for how to couple σ to ψ, we begin for simplicity ... |

132 |
Emergent quantum criticality, Fermi surfaces
- Faulkner, Liu, et al.
(Show Context)
Citation Context ...s in the 0 + 1 dimensional CFT dual to this region. This is closely analogous to the way properties of holographic non-Fermi liquids [8, 9, 10] were described in terms of a dual 0 + 1 dimensional CFT =-=[11, 12]-=-. In addition, the instability for κ < κc can be interpreted as turning on a double trace term with negative coefficient in the 0 + 1 dimensional CFT dual to this region. Let us contrast this with the... |

119 |
Multi-trace operators, boundary conditions, and AdS/CFT correspondence,” arXiv:hep-th/0112258. 32
- Witten
(Show Context)
Citation Context ... BF bound which are allowed due to modified boundary conditions for the scalar field. The boundary conditions may be modified due to the addition of a multi-trace deformation in the dual field theory =-=[15, 16]-=-, or simply due to alternative quantization of the bulk theory [17]. It was widely believed that if one added a double trace term with κ < 0, then the theory would not have a stable ground state. Howe... |

99 | Curvature singularities: the good, the bad, and the naked,”
- Gubser
- 2000
(Show Context)
Citation Context ...l refer to this solution as ÃdS2. 12Another possibility, outlined recently in [45], is that a curvature singularity develops in the IR which sources the gauge field, one which is physically sensible =-=[46]-=-. Such behavior was seen for unbounded potentials at q = 0 in [44], though not thoroughly understood. This would be an interesting state to consider since then the ordered phase could be insulating (g... |

93 |
A Non-Fermi Liquid from a Charged Black Hole: A Critical Fermi Ball,” Phys
- Lee
(Show Context)
Citation Context ...es, but are determined by the scaling dimension of certain operators in the 0 + 1 dimensional CFT dual to this region. This is closely analogous to the way properties of holographic non-Fermi liquids =-=[8, 9, 10]-=- were described in terms of a dual 0 + 1 dimensional CFT [11, 12]. In addition, the instability for κ < κc can be interpreted as turning on a double trace term with negative coefficient in the 0 + 1 d... |

91 | Introduction to holographic superconductors,”
- Horowitz
- 2011
(Show Context)
Citation Context ...ing the theory when a magnetic field is turned on is often difficult, due to the formation of superconducting droplets at nonzero q. However, we can study the theory near the critical point following =-=[1, 51]-=- by studying linearized analysis around a dyonic black hole. The dyonic RN AdS black hole15 is a simple generalization of (2.18), which now we are writing in terms of the horizon radius r0, the chemic... |

86 |
Universality of the hydrodynamic limit
- Iqbal, Liu
(Show Context)
Citation Context ... that β̂0/α̂0 = ΣR(ω) where ΣR is the retarded AdS2 Green’s function for fluctuations on the background (3.2). The Green’s function in the full CFT can be computed using any of the usual prescription =-=[37, 38]-=- generalized to include nonstandard boundary conditions. The result is up to overall normalization, χR(ω, ~p) = α −β + κα = Z + . . . κIR − ΣR(ω) + X(ω, ~p) + . . . Z = (a +)2/ detL (3.9) where we hav... |

85 |
Ohm’s Law at strong coupling: S duality and the cyclotron resonance,” Phys
- Hartnoll, Herzog
(Show Context)
Citation Context ... ) , (5.11) where again δ± = 12 ± √ 1 4 +m2eff is the infrared dimension. It is clear that turning on a magnetic field changes the infrared dimension of the operator, and can possibly change it 15See =-=[52]-=- for a detailed study of the transport properties of the dyonic black hole. 39 from real to complex16. This defines a critical magnetization where m2eff = −1/4, Mc = µ √ 12g − 2m2 − 3 12g + 2m2 + 3 , ... |

70 |
A universal result on central charges in the presence of double-trace deformations,” Nucl. Phys. B656
- Gubser, Klebanov
- 2003
(Show Context)
Citation Context ...e theory with standard boundary conditions. If we had started with κ = 0 we would stay at the unstable fixed point in alternative quantization. Many details of this flow have been studied (see, e.g., =-=[31]-=-). 2.2 Symmetry breaking from double trace deformations We will first study a simple model of spontaneous symmetry breaking. We will work with zero chemical potential, and hence can set the bulk Maxwe... |

64 |
Double-trace deformations, boundary conditions and spacetime singularities
- Berkooz, Sever, et al.
(Show Context)
Citation Context ... BF bound which are allowed due to modified boundary conditions for the scalar field. The boundary conditions may be modified due to the addition of a multi-trace deformation in the dual field theory =-=[15, 16]-=-, or simply due to alternative quantization of the bulk theory [17]. It was widely believed that if one added a double trace term with κ < 0, then the theory would not have a stable ground state. Howe... |

63 |
Non-Fermi liquids from holography,” arXiv:0903.2477 [hep-th
- Liu, McGreevy, et al.
(Show Context)
Citation Context ...es, but are determined by the scaling dimension of certain operators in the 0 + 1 dimensional CFT dual to this region. This is closely analogous to the way properties of holographic non-Fermi liquids =-=[8, 9, 10]-=- were described in terms of a dual 0 + 1 dimensional CFT [11, 12]. In addition, the instability for κ < κc can be interpreted as turning on a double trace term with negative coefficient in the 0 + 1 d... |

61 |
Dynamics in nonglobally hyperbolic static space-times.
- Ishibashi, Wald
- 2004
(Show Context)
Citation Context ...er, for κ < 0, we have a tachyonic instability, with a pole at real positive p2pole. All of this is directly analogous to a massless free scalar field getting a massive deformation of either sign. In =-=[32]-=- an exponentially growing tachyonic mode was explicitly found in the bulk 2This can be calculated either in the field theory at large N by summing up a geometric series of diagrams, or on the gravity ... |

60 |
Ground states of holographic superconductors,” Phys
- Gubser, Nellore
(Show Context)
Citation Context ...ationship which can be derived analogous to the above manipulations. The result is, 30 m0 = 2 3 (µρ+ Ts) → gW = −1 3 (Ts+ µρ) + 2(∆+ −∆−) ( −1 3 ∆−αβ +W (α) ) (4.16) The first equation was derived in =-=[42]-=- using the Noether charge associated with the conformal rescaling. Practically speaking these last two equations are the most useful for reading off the free energy from numerical data. Since the m0 c... |

55 |
String Theory
- Cubrovic, Zaanen, et al.
(Show Context)
Citation Context ...es, but are determined by the scaling dimension of certain operators in the 0 + 1 dimensional CFT dual to this region. This is closely analogous to the way properties of holographic non-Fermi liquids =-=[8, 9, 10]-=- were described in terms of a dual 0 + 1 dimensional CFT [11, 12]. In addition, the instability for κ < κc can be interpreted as turning on a double trace term with negative coefficient in the 0 + 1 d... |

38 |
Landscape of superconducting membranes,” Phys
- Denef, Hartnoll
(Show Context)
Citation Context ...ient in the 0 + 1 dimensional CFT dual to this region. Let us contrast this with the usual argument for why the RN AdS black hole becomes unstable at low temperature in the presence of a scalar field =-=[13]-=-. In the AdS2 near horizon geometry of the T = 0 solution, the scalar field has an effective mass meff which depends on the original mass m and charge q of the scalar field. When this effective mass s... |

38 |
Holographic description of AdS cosmologies,
- Hertog, Horowitz
- 2005
(Show Context)
Citation Context ...oblem. Another way of studying this system at T > 0 is to construct the finite temperature generalization of V . This can be obtained from the family of hairy black holes in the bulk, as described in =-=[33]-=-. 2.3 A novel holographic superconductor We saw above that adding a renormalizable double trace coupling can break a U(1) symmetry at low temperature. This provides a new mechanism for constructing ho... |

37 |
Quantum critical superconductors in string theory and M-theory,” Phys
- Gubser, Pufu, et al.
(Show Context)
Citation Context ... phase (Schwarzschild AdS solution) and the black line is the free energy of the condensed phase. We used a case with ∆− = 1, and bulk potential V (ψ) = sinh2(ψ/ √ 2)(cosh( √ 2ψ)− 5) = −6− 2ψ2 +O(ψ4) =-=[34, 35]-=-. In [18] it was found that sc = 0.56 for this potential. From (2.15), we have Tc/(−κ) ≈ 0.62. metric. As shown in Appendix A, the conductivity can be simply related to the reflection coefficient in a... |

35 |
E↵ect of a nonzero temperature on quantum critical points in itinerant fermion systems
- Millis
- 1993
(Show Context)
Citation Context ...mind, in particular so we can compare our results to quantum phase transitions in metallic systems, where anti-ferromagnetic order plays an important role. The “standard” theory of which was given in =-=[21, 22]-=- is based on the renormalization group Landau-Ginzburg paradigm. However experimental measurements (see for example [23, 24], and references therein) of heavy fermion systems with quantum critical poi... |

32 |
Phase transitions between ReissnerNordstrom and dilatonic black holes
- Cadoni, D’Appollonio, et al.
- 2010
(Show Context)
Citation Context ...uction arose since a state with net charge can be boosted, yielding a 5Since the Schrodinger potential is no longer positive definite, one can sometimes get peaks at low frequency in the conductivity =-=[36]-=-. 10 nonzero current with zero applied electric field. This implies infinite DC conductivity. Since we can now start in a state with zero charge, we no longer have this problem. Mathematically, the de... |

31 |
Holographic BerezinskiiKosterlitz-Thouless Transitions
- Jensen, Karch, et al.
(Show Context)
Citation Context ...l magnetization where m2eff = −1/4, Mc = µ √ 12g − 2m2 − 3 12g + 2m2 + 3 , (5.12) where there is an infinite order holographic BKT transition 17, just as that found in [40, 19] and studied further in =-=[53, 54, 55]-=- (for a field theoretic discussion see [56].) The critical point at κ = κc turns into a second order phase boundary, which terminates at Mc. See figure 14 for example phase diagrams. XO\ 0, ∆- Compl... |

29 |
Quantum critical phenomena,” Phys
- Hertz
- 1976
(Show Context)
Citation Context ...mind, in particular so we can compare our results to quantum phase transitions in metallic systems, where anti-ferromagnetic order plays an important role. The “standard” theory of which was given in =-=[21, 22]-=- is based on the renormalization group Landau-Ginzburg paradigm. However experimental measurements (see for example [23, 24], and references therein) of heavy fermion systems with quantum critical poi... |

23 |
Phase diagram of the D3/D5 system in a magnetic field and a BKT transition
- Evans, Gebauer, et al.
(Show Context)
Citation Context ...l magnetization where m2eff = −1/4, Mc = µ √ 12g − 2m2 − 3 12g + 2m2 + 3 , (5.12) where there is an infinite order holographic BKT transition 17, just as that found in [40, 19] and studied further in =-=[53, 54, 55]-=- (for a field theoretic discussion see [56].) The critical point at κ = κc turns into a second order phase boundary, which terminates at Mc. See figure 14 for example phase diagrams. XO\ 0, ∆- Compl... |

22 |
Holographic superconductivity
- Gauntlett, Sonner, et al.
(Show Context)
Citation Context ... phase (Schwarzschild AdS solution) and the black line is the free energy of the condensed phase. We used a case with ∆− = 1, and bulk potential V (ψ) = sinh2(ψ/ √ 2)(cosh( √ 2ψ)− 5) = −6− 2ψ2 +O(ψ4) =-=[34, 35]-=-. In [18] it was found that sc = 0.56 for this potential. From (2.15), we have Tc/(−κ) ≈ 0.62. metric. As shown in Appendix A, the conductivity can be simply related to the reflection coefficient in a... |

22 | Black hole determinants and quasinormal modes,” arXiv:0908.2657 [hep-th
- Denef, Hartnoll, et al.
(Show Context)
Citation Context ...tart by considering the disordered phase. Firstly it would be interesting to understand one loop corrections to the thermodynamics and transport that come from fluctuations of ψ. Methods developed in =-=[57, 58, 59, 60, 12, 61]-=- would be useful for this purpose. In the large N limit, quite often bulk geometric contributions to thermodynamics and transport dominate since they are of order 1/GN , so 1 loop contributions which ... |

21 |
Condensed matter and AdS/CFT,” arXiv:1002.2947 [hep-th
- Sachdev
(Show Context)
Citation Context ...Complete AdS4 expansion and boundary terms 51 1 Introduction Over the past couple of years, gauge/gravity duality has been applied to a number of problems in condensed matter physics (for reviews see =-=[1, 2, 3]-=-). An important feature of some condensed matter systems is the existence of quantum critical points, marking continuous phase transitions at zero temperature. One goal of the present work is to intro... |

21 |
Quantum criticality in heavy-fermion metals
- Gegenwart, Si, et al.
- 2008
(Show Context)
Citation Context ... order plays an important role. The “standard” theory of which was given in [21, 22] is based on the renormalization group Landau-Ginzburg paradigm. However experimental measurements (see for example =-=[23, 24]-=-, and references therein) of heavy fermion systems with quantum critical points show that the “standard” theory can break down, as a result new theoretical methods are required. Subsequently several d... |

17 |
Locally critical quantum phase transitions in strongly correlated metals
- Si, Rabello, et al.
(Show Context)
Citation Context ...s with quantum critical points show that the “standard” theory can break down, as a result new theoretical methods are required. Subsequently several different methods were developed (see for example =-=[25, 26, 27, 28]-=-.) One such method [25, 26] which is formally justified in a large d expansion [29] shows local quantum critical behavior similar to the new quantum critical point that we find. It will be useful to c... |

14 |
Semi-Holographic Fermi Liquids,” [arXiv:1001.5049 [hepth
- Faulkner, Polchinski
(Show Context)
Citation Context ...r region we find for the IR limit of the two point function, χR = Z κIR + cp~p2 − T 2/zg(ω/T, ~p2/T 2/zG) (5.19) where z = 2/(δ+ − δ−). Note that this result can also be obtained semi-holographically =-=[20]-=-. Again there should be some matching between κIR and (κ − κc) in the outer region. Importantly we have included an analytic in ~p2 correction which will also come from the outer region. This correcti... |

13 | New stability results for einstein scalar gravity
- Faulkner, Horowitz, et al.
(Show Context)
Citation Context ...]. It was widely believed that if one added a double trace term with κ < 0, then the theory would not have a stable ground state. However, we have recently shown that this is not necessarily the case =-=[18]-=-. For a large class of dual gravity theories, there is still a stable ground state with 〈O〉 6= 0 when the boundary conditions correspond to κ < 0. As one increases the temperature, there is a second o... |

13 |
Nature 407
- Schröder, Aeppli, et al.
- 2000
(Show Context)
Citation Context ...stence of the locally critical modes associated with AdS2. These results are compatible with experimental measurements of the spin susceptibility in a heavy fermion compound CeCu6−xAux at criticality =-=[39]-=-. In order to compare the spin susceptibility to the two point function of the triplet staggered order parameter (which is effectively χR), one must shift the momentum in (3.22) by the ordering vector... |

13 | Magnetic Field Induced Quantum Criticality via new Asymptotically AdS5 Solutions
- D’Hoker, Kraus
- 2010
(Show Context)
Citation Context ...gested by Fig. 6 there will be two tuning parameters, of which only an appropriate scale 10A similar argument appeared in [40] in the context of a BKT type transition, and related arguments appear in =-=[41]-=-. 21 κIR δY 2 1 AdS(std) δ ψ=0 µ κ δh δ X 2µY (std) 4AdS (alt) 4AdS AdS (alt)2 ψ=0 Figure 6: Renormalization group flow interpretation of the quantum critical point (denoted by the red dot) for 0 < δ−... |

13 |
Condensed matter physics of a strongly coupled gauge theory with quarks: some novel features of the phase diagram
- Faulkner, Liu
(Show Context)
Citation Context ...g functions V,G, J and the IR geometry X will not be important for understanding physics near the critical point. Although, as already mentioned, there are a 14Similar “3 shelf” structure was seen in =-=[47]-=- for a probe brane model. It would be interesting to understand better the critical theory involved in that case. 35 -8 -6 -4 -2 0 2 -10 -5 0 lnHΚc-ΚL ln < O > -8 -6 -4 -2 0 2 -30 -20 -10 0 10 lnHΚc-Κ... |

11 |
Weak magnetism and non-fermi liquids near heavy-fermion critical points
- Senthil, Vojta, et al.
- 2004
(Show Context)
Citation Context ...s with quantum critical points show that the “standard” theory can break down, as a result new theoretical methods are required. Subsequently several different methods were developed (see for example =-=[25, 26, 27, 28]-=-.) One such method [25, 26] which is formally justified in a large d expansion [29] shows local quantum critical behavior similar to the new quantum critical point that we find. It will be useful to c... |

10 | Generalized lifshitz-kosevich scaling at quantum criticality from the holographic correspondence. Phys. Rev. B. http: // journals. aps. org/ prb/ abstract/ 10
- Hartnoll
(Show Context)
Citation Context ...tart by considering the disordered phase. Firstly it would be interesting to understand one loop corrections to the thermodynamics and transport that come from fluctuations of ψ. Methods developed in =-=[57, 58, 59, 60, 12, 61]-=- would be useful for this purpose. In the large N limit, quite often bulk geometric contributions to thermodynamics and transport dominate since they are of order 1/GN , so 1 loop contributions which ... |

9 | Multitrace deformations, gamow states, and stability of ads/cft - Vecchi |

9 |
Energy Bounds in Designer Gravity,” Phys
- Amsel, Marolf
- 2006
(Show Context)
Citation Context ... be complete up to and including O(r−3) assuming that 3/2 < ∆+ < 3. To this order, it suffices to take G = 1 and J = ψ2. The result is only a slight generalization of expressions that can be found in =-=[66]-=-. The generalization consists of allowing for a nonzero chemical potential (we also work in a different coordinate system.) These are then used to compute the on shell action and boundary terms that a... |

7 |
Holography and the Coleman-Mermin-Wagner theorem,” Phys
- Anninos, Hartnoll, et al.
- 2010
(Show Context)
Citation Context ...tart by considering the disordered phase. Firstly it would be interesting to understand one loop corrections to the thermodynamics and transport that come from fluctuations of ψ. Methods developed in =-=[57, 58, 59, 60, 12, 61]-=- would be useful for this purpose. In the large N limit, quite often bulk geometric contributions to thermodynamics and transport dominate since they are of order 1/GN , so 1 loop contributions which ... |

6 | The Particle number in Galilean holography
- Balasubramanian, McGreevy
(Show Context)
Citation Context ..., at zero temperature, there must necessarily be an AdS2 × R2 solution in the IR, with constant scalar field [19]. We will refer to this solution as ÃdS2. 12Another possibility, outlined recently in =-=[45]-=-, is that a curvature singularity develops in the IR which sources the gauge field, one which is physically sensible [46]. Such behavior was seen for unbounded potentials at q = 0 in [44], though not ... |

5 |
Quantum phase transition in a Dp-Dq system,” Phys
- Pal
- 2010
(Show Context)
Citation Context ...l magnetization where m2eff = −1/4, Mc = µ √ 12g − 2m2 − 3 12g + 2m2 + 3 , (5.12) where there is an infinite order holographic BKT transition 17, just as that found in [40, 19] and studied further in =-=[53, 54, 55]-=- (for a field theoretic discussion see [56].) The critical point at κ = κc turns into a second order phase boundary, which terminates at Mc. See figure 14 for example phase diagrams. XO\ 0, ∆- Compl... |

4 |
J.L.: Local fluctuations in quantum critical metals
- Si, Rabello, et al.
- 2003
(Show Context)
Citation Context ...s with quantum critical points show that the “standard” theory can break down, as a result new theoretical methods are required. Subsequently several different methods were developed (see for example =-=[25, 26, 27, 28]-=-.) One such method [25, 26] which is formally justified in a large d expansion [29] shows local quantum critical behavior similar to the new quantum critical point that we find. It will be useful to c... |

4 |
Fractionalized Fermi liquids
- Senthil, Sachdev, et al.
(Show Context)
Citation Context |

2 |
Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators
- Yamamoto, Si
(Show Context)
Citation Context ...earn something about the mysterious CFT dual to AdS2 × R2. Such possibilities were discussed recently in a related context [49]. The relationship of AdS2 to local quantum criticality was discussed in =-=[50]-=-. We now would like to discuss some immediate generalizations. 5.3 Magnetic fields Studying the theory when a magnetic field is turned on is often difficult, due to the formation of superconducting dr... |