Abstract
Using high-precision numerical analysis, we show that 3+1 dimensional gauge theories holographically dual to 4 + 1 dimensional Einstein-Maxwell-Chern-Simons theory undergo a quantum phase transition in the presence of a finite charge density and magnetic field. The quantum critical theory has dynamical scaling exponent z = 3, and is reached by tuning a relevant operator of scaling dimension 2. For magnetic field B above the critical value B c , the system behaves as a Fermi liquid. As the magnetic field approaches B c from the high field side, the specific heat coefficient diverges as 1/(B - B c ), and non-Fermi liquid behavior sets in. For B < B c the entropy density s becomes non-vanishing at zero temperature, and scales according to \( s \sim \sqrt {{B_c} - B} \). At B = B c , and for small non-zero temperature T, a new scaling law sets in for which s ∼ T 1/3. Throughout a small region surrounding the quantum critical point, the ratio s/T 1/3 is given by a universal scaling function which depends only on the ratio (B - B c )/T 2/3.
The quantum phase transition involves non-analytic behavior of the specific heat and magnetization but no change of symmetry. Above the critical field, our numerical results are consistent with those predicted by the Hertz/Millis theory applied to metamagnetic quantum phase transitions, which also describe non-analytic changes in magnetization without change of symmetry. Such transitions have been the subject of much experimental investigation recently, especially in the compound Sr3Ru2O7, and we comment on the connections.
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References
A. Buchel and J.T. Liu, Gauged supergravity from type IIB string theory on Y(p,q) manifolds, Nucl. Phys. B 771 (2007) 93 [hep-th/0608002] [SPIRES].
J.P. Gauntlett, E. O Colgain and O. Varela, Properties of some conformal field theories with M-theory duals, JHEP 02 (2007) 049 [hep-th/0611219] [SPIRES].
J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions, Phys. Rev. D 76 (2007) 126007 [arXiv:0707.2315] [SPIRES].
S. Sachdev, Quantum Phase Transitions, Cambridge University Press, Cambridge, U.K. (2001).
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, arXiv:0903.2477 [SPIRES].
M. Cubrovic, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science 325 (2009) 439 [arXiv:0904.1993] [SPIRES].
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, arXiv:0907.2694 [SPIRES].
T. Faulkner and J. Polchinski, Semi-Holographic Fermi Liquids, arXiv:1001.5049 [SPIRES].
S.-J. Rey, String theory on thin semiconductors: Holographic realization of Fermi points and surfaces, Prog. Theor. Phys. Suppl. 177 (2009) 128 [arXiv:0911.5295] [SPIRES].
E. D'Hoker and P. Kraus, Magnetic Brane Solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [SPIRES].
E. D'Hoker and P. Kraus, Charged Magnetic Brane Solutions in AdS 5 and the fate of the third law of thermodynamics, JHEP 03 (2010) 095 [arXiv:0911.4518] [SPIRES].
D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, Warped AdS 3 Black Holes, JHEP 03 (2009) 130 [arXiv:0807.3040] [SPIRES].
G. Compere and S. Detournay, Boundary conditions for spacelike and timelike warped AdS 3 spaces in topologically massive gravity, JHEP 08 (2009) 092 [arXiv:0906.1243] [SPIRES].
A.J. Millis, A.J. Schofield, G.G. Lonzarich and S.A. Grigera, Metamagnetic quantum criticality in metals, Phys. Rev. Lett. 88 (2002) 217204 [cond-mat/0109440].
A.W. Rost, R.S. Perry, J.-F. Mercure, A.P. Mackenzie, and S.A. Grigera, Entropy Landscape of Phase Formation Associated with Quantum Criticality in Sr 3 Ru 2 O 7 , Science 325 (2009) 1360.
G. Lifschytz and M. Lippert, Holographic Magnetic Phase Transition, Phys. Rev. D 80 (2009) 066007 [arXiv:0906.3892] [SPIRES].
J.A. Hertz, Quantum critical phenomena, Phys. Rev. B 14 (1976) 1165 [SPIRES].
A.J. Millis, Effect of a nonzero temperature on quantum critical points in itinerant fermion systems, Phys. Rev. B 48 (1993) 7183.
H.v. Lohneysen, A. Rosch, M. Vojta and P. Wole, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys. 79 (2007) 1015 [SPIRES].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [SPIRES].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [SPIRES].
A. Parnachev and D.A. Sahakyan, Chiral phase transition from string theory, Phys. Rev. Lett. 97 (2006) 111601 [hep-th/0604173] [SPIRES].
D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [SPIRES].
J.L. Davis, M. Gutperle, P. Kraus and I. Sachs, Stringy NJL and Gross-Neveu models at finite density and temperature, JHEP 10 (2007) 049 [arXiv:0708.0589] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].
J.L. Davis, P. Kraus and A. Shah, Gravity Dual of a Quantum Hall Plateau Transition, JHEP 11 (2008) 020 [arXiv:0809.1876] [SPIRES].
N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Holographic Description of the Phase Diagram of a Chiral Symmetry Breaking Gauge Theory, JHEP 03 (2010) 132 [1002.1885] [SPIRES].
K. Jensen, A. Karch and e.g. Thompson, A Holographic Quantum Critical Point at Finite Magnetic Field and Finite Density, JHEP 05 (2010) 015 [1002.2447] [SPIRES].
G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [SPIRES].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, arXiv:0911.3586 [SPIRES].
M. Cadoni, G. D'Appollonio and P. Pani, Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime, JHEP 03 (2010) 100 [arXiv:0912.3520] [SPIRES].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [SPIRES].
V. Oganesyan, S.A. Kivelson and E. Fradkin, Quantum theory of a nematic Fermi fuid, Phys. Rev. B 64 (2001) 195109 [cond-mat/0102093].
E. Fradkin, S.A. Kivelson, M.J. Lawler, J.P. Eisenstein, and A.P. Mackenzie, Nematic Fermi Fluids in Condensed Matter Physics, arXiv:0910.4166.
S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [SPIRES].
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ArXiv ePrint: 1003.1302
This work was supported in part by NSF grant PHY-07-57702.
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D’Hoker, E., Kraus, P. Holographic metamagnetism, quantum criticality, and crossover behavior. J. High Energ. Phys. 2010, 83 (2010). https://doi.org/10.1007/JHEP05(2010)083
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DOI: https://doi.org/10.1007/JHEP05(2010)083