Abstract
We study the thermoelectric DC conductivities of Horndeski holographic models with momentum dissipation. We compute the butterfly velocity v B and we discuss the existence of universal bounds on charge and energy diffusivities in the incoherent limit related to quantum chaos. We find that the Horndeski coupling represents a subleading contribution to the thermoelectric conductivities in the incoherent limit and therefore it does not affect any of the proposed bounds.
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S. Sachdev and B. Keimer, Quantum criticality, Phys. Today 64 (2011) 29 [arXiv:1102.4628] [INSPIRE].
J.A.N. Bruin, H. Sakai, R.S. Perry and A.P. Mackenzie, Similarity of scattering rates in metals showing T -linear resistivity, Science 339 (2013) 804.
J.C. Zhang et al., Anomalous thermal diffusivity in underdoped YBa 2 Cu 3 O 6+x , Proc. Nat. Acad. Sci. 114 (2017) 5378 [arXiv:1610.05845] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
S. Grozdanov, A. Lucas, S. Sachdev and K. Schalm, Absence of disorder-driven metal-insulator transitions in simple holographic models, Phys. Rev. Lett. 115 (2015) 221601 [arXiv:1507.00003] [INSPIRE].
S. Grozdanov, A. Lucas and K. Schalm, Incoherent thermal transport from dirty black holes, Phys. Rev. D 93 (2016) 061901 [arXiv:1511.05970] [INSPIRE].
K. Bitaghsir Fadafan, Conductivity bound from dirty black holes, Phys. Lett. B 762 (2016) 399 [arXiv:1602.05943] [INSPIRE].
A. Lucas and S.A. Hartnoll, Resistivity bound for hydrodynamic bad metals, arXiv:1704.07384 [INSPIRE].
S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].
A. Amoretti, A. Braggio, N. Magnoli and D. Musso, Bounds on charge and heat diffusivities in momentum dissipating holography, JHEP 07 (2015) 102 [arXiv:1411.6631] [INSPIRE].
M. Blake, Universal charge diffusion and the butterfly effect in holographic theories, Phys. Rev. Lett. 117 (2016) 091601 [arXiv:1603.08510] [INSPIRE].
M. Blake, Universal diffusion in incoherent black holes, Phys. Rev. D 94 (2016) 086014 [arXiv:1604.01754] [INSPIRE].
D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP 03 (2015) 051 [arXiv:1409.8180] [INSPIRE].
D.A. Roberts and B. Swingle, Lieb-Robinson bound and the butterfly effect in quantum field theories, Phys. Rev. Lett. 117 (2016) 091602 [arXiv:1603.09298] [INSPIRE].
Y. Ling, P. Liu and J.-P. Wu, Note on the butterfly effect in holographic superconductor models, Phys. Lett. B 768 (2017) 288 [arXiv:1610.07146] [INSPIRE].
Y. Ling, P. Liu and J.-P. Wu, Holographic butterfly effect at quantum critical points, arXiv:1610.02669 [INSPIRE].
R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: the Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].
K.-Y. Kim and C. Niu, Diffusion and butterfly velocity at finite density, JHEP 06 (2017) 030 [arXiv:1704.00947] [INSPIRE].
Y. Gu, X.-L. Qi and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, JHEP 05 (2017) 125 [arXiv:1609.07832] [INSPIRE].
I.L. Aleiner, L. Faoro and L.B. Ioffe, Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves, Annals Phys. 375 (2016) 378 [arXiv:1609.01251] [INSPIRE].
B. Swingle and D. Chowdhury, Slow scrambling in disordered quantum systems, Phys. Rev. B 95 (2017) 060201 [arXiv:1608.03280] [INSPIRE].
A.A. Patel and S. Sachdev, Quantum chaos on a critical Fermi surface, Proc. Nat. Acad. Sci. 114 (2017) 1844 [arXiv:1611.00003] [INSPIRE].
A. Bohrdt, C.B. Mendl, M. Endres and M. Knap, Scrambling and thermalization in a diffusive quantum many-body system, New J. Phys. 19 (2017) 063001 [arXiv:1612.02434] [INSPIRE].
Y. Werman, S.A. Kivelson and E. Berg, Quantum chaos in an electron-phonon bad metal, arXiv:1705.07895 [INSPIRE].
M. Blake and A. Donos, Quantum critical transport and the Hall angle, Phys. Rev. Lett. 114 (2015) 021601 [arXiv:1406.1659] [INSPIRE].
A. Amoretti, M. Baggioli, N. Magnoli and D. Musso, Chasing the cuprates with dilatonic dyons, JHEP 06 (2016) 113 [arXiv:1603.03029] [INSPIRE].
A. Lucas, Conductivity of a strange metal: from holography to memory functions, JHEP 03 (2015) 071 [arXiv:1501.05656] [INSPIRE].
A. Lucas, Hydrodynamic transport in strongly coupled disordered quantum field theories, New J. Phys. 17 (2015) 113007 [arXiv:1506.02662] [INSPIRE].
R.A. Davison and B. Goutéraux, Dissecting holographic conductivities, JHEP 09 (2015) 090 [arXiv:1505.05092] [INSPIRE].
M. Baggioli and O. Pujolàs, On holographic disorder-driven metal-insulator transitions, JHEP 01 (2017) 040 [arXiv:1601.07897] [INSPIRE].
B. Goutéraux, E. Kiritsis and W.-J. Li, Effective holographic theories of momentum relaxation and violation of conductivity bound, JHEP 04 (2016) 122 [arXiv:1602.01067] [INSPIRE].
M. Baggioli, B. Goutéraux, E. Kiritsis and W.-J. Li, Higher derivative corrections to incoherent metallic transport in holography, JHEP 03 (2017) 170 [arXiv:1612.05500] [INSPIRE].
A.M. García-García, B. Loureiro and A. Romero-Bermúdez, Transport in a gravity dual with a varying gravitational coupling constant, Phys. Rev. D 94 (2016) 086007 [arXiv:1606.01142] [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
E. Kiritsis and J. Ren, On holographic insulators and supersolids, JHEP 09 (2015) 168 [arXiv:1503.03481] [INSPIRE].
M. Baggioli and O. Pujolàs, On effective holographic Mott insulators, JHEP 12 (2016) 107 [arXiv:1604.08915] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
M. Baggioli and O. Pujolàs, Electron-phonon interactions, metal-insulator transitions and holographic massive gravity, Phys. Rev. Lett. 114 (2015) 251602 [arXiv:1411.1003] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
A. Donos, B. Goutéraux and E. Kiritsis, Holographic metals and insulators with helical symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].
A. Lucas and J. Steinberg, Charge diffusion and the butterfly effect in striped holographic matter, JHEP 10 (2016) 143 [arXiv:1608.03286] [INSPIRE].
Y. Gu, A. Lucas and X.-L. Qi, Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains, SciPost Phys. 2 (2017) 018 [arXiv:1702.08462] [INSPIRE].
L. Cheng, X.-H. Ge and Z.-Y. Sun, Thermoelectric DC conductivities with momentum dissipation from higher derivative gravity, JHEP 04 (2015) 135 [arXiv:1411.5452] [INSPIRE].
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].
C. Deffayet and D.A. Steer, A formal introduction to Horndeski and Galileon theories and their generalizations, Class. Quant. Grav. 30 (2013) 214006 [arXiv:1307.2450] [INSPIRE].
T.P. Sotiriou and S.-Y. Zhou, Black hole hair in generalized scalar-tensor gravity, Phys. Rev. Lett. 112 (2014) 251102 [arXiv:1312.3622] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].
C. Charmousis, B. Gouteraux and E. Kiritsis, Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography, JHEP 09 (2012) 011 [arXiv:1206.1499] [INSPIRE].
X.-H. Feng, H.-S. Liu, H. Lü and C.N. Pope, Black hole entropy and viscosity bound in Horndeski gravity, JHEP 11 (2015) 176 [arXiv:1509.07142] [INSPIRE].
X.-H. Feng, H.-S. Liu, H. Lü and C.N. Pope, Thermodynamics of charged black holes in Einstein-Horndeski-Maxwell theory, Phys. Rev. D 93 (2016) 044030 [arXiv:1512.02659] [INSPIRE].
L. Alberte, M. Baggioli, A. Khmelnitsky and O. Pujolàs, Solid holography and massive gravity, JHEP 02 (2016) 114 [arXiv:1510.09089] [INSPIRE].
M. Blake, D. Tong and D. Vegh, Holographic lattices give the graviton an effective mass, Phys. Rev. Lett. 112 (2014) 071602 [arXiv:1310.3832] [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli and D. Musso, Analytic DC thermoelectric conductivities in holography with massive gravitons, Phys. Rev. D 91 (2015) 025002 [arXiv:1407.0306] [INSPIRE].
W.-J. Jiang, H.-S. Liu, H. Lü and C.N. Pope, DC conductivities with momentum dissipation in Horndeski theories, arXiv:1703.00922 [INSPIRE].
X.-M. Kuang and E. Papantonopoulos, Building a holographic superconductor with a scalar field coupled kinematically to Einstein tensor, JHEP 08 (2016) 161 [arXiv:1607.04928] [INSPIRE].
A. Anabalon, A. Cisterna and J. Oliva, Asymptotically locally AdS and flat black holes in Horndeski theory, Phys. Rev. D 89 (2014) 084050 [arXiv:1312.3597] [INSPIRE].
A. Cisterna and C. Erices, Asymptotically locally AdS and flat black holes in the presence of an electric field in the Horndeski scenario, Phys. Rev. D 89 (2014) 084038 [arXiv:1401.4479] [INSPIRE].
A. Donos, J.P. Gauntlett, T. Griffin, N. Lohitsiri and L. Melgar, Holographic DC conductivity and Onsager relations, JHEP 07 (2017) 006 [arXiv:1704.05141] [INSPIRE].
M. Blake, A. Donos and N. Lohitsiri, Magnetothermoelectric response from holography, JHEP 08 (2015) 124 [arXiv:1502.03789] [INSPIRE].
A. Amoretti and D. Musso, Magneto-transport from momentum dissipating holography, JHEP 09 (2015) 094 [arXiv:1502.02631] [INSPIRE].
A. Amoretti, A. Braggio, N. Maggiore and N. Magnoli, Thermo-electric transport in gauge/gravity models, Adv. Phys. X 2 (2017) 409 [INSPIRE].
A. Lucas and S. Sachdev, Memory matrix theory of magnetotransport in strange metals, Phys. Rev. B 91 (2015) 195122 [arXiv:1502.04704] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Coherent/incoherent metal transition in a holographic model, JHEP 12 (2014) 170 [arXiv:1409.8346] [INSPIRE].
X.-H. Ge, Y. Ling, C. Niu and S.-J. Sin, Thermoelectric conductivities, shear viscosity and stability in an anisotropic linear axion model, Phys. Rev. D 92 (2015) 106005 [arXiv:1412.8346] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Thermoelectric conductivities at finite magnetic field and the Nernst effect, JHEP 07 (2015) 027 [arXiv:1502.05386] [INSPIRE].
L. Alberte, M. Baggioli and O. Pujolàs, Viscosity bound violation in holographic solids and the viscoelastic response, JHEP 07 (2016) 074 [arXiv:1601.03384] [INSPIRE].
M. Blake and A. Donos, Diffusion and chaos from near AdS 2 horizons, JHEP 02 (2017) 013 [arXiv:1611.09380] [INSPIRE].
S.-F. Wu, B. Wang, X.-H. Ge and Y. Tian, Universal diffusion in strange-metal transport, arXiv:1702.08803 [INSPIRE].
R.A. Davison, B. Goutéraux and S.A. Hartnoll, Incoherent transport in clean quantum critical metals, JHEP 10 (2015) 112 [arXiv:1507.07137] [INSPIRE].
M. Baggioli and D.K. Brattan, Drag phenomena from holographic massive gravity, Class. Quant. Grav. 34 (2017) 015008 [arXiv:1504.07635] [INSPIRE].
M. Baggioli and W.-J. Li, η/s bound with broken symmetries, work in progress.
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
M. Visser, Dirty black holes: entropy as a surface term, Phys. Rev. D 48 (1993) 5697 [hep-th/9307194] [INSPIRE].
R. Brustein, D. Gorbonos and M. Hadad, Wald’s entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling, Phys. Rev. D 79 (2009) 044025 [arXiv:0712.3206] [INSPIRE].
M. Alishahiha, A. Davody, A. Naseh and S.F. Taghavi, On butterfly effect in higher derivative gravities, JHEP 11 (2016) 032 [arXiv:1610.02890] [INSPIRE].
S.H. Shenker and D. Stanford, Multiple shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE].
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Baggioli, M., Li, WJ. Diffusivities bounds and chaos in holographic Horndeski theories. J. High Energ. Phys. 2017, 55 (2017). https://doi.org/10.1007/JHEP07(2017)055
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DOI: https://doi.org/10.1007/JHEP07(2017)055