Quantum criticality and black holes

Abstract

Abstract. Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport co-efficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the AdS/CFT duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport co-efficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance.Plenary talk at the 25th International Conference on Low Temperature Physics, Amsterdam, 6-13 Aug 2008. IntroductionA major focus of research in condensed matter physics is on systems which are not described by the familiar paradigms of order parameters and quasiparticles. In states with broken symmetry, we focus on the order parameter which characterizes the broken symmetry, and work with effective classical equations of motion for the order parameter. In states with long-lived quasiparticle excitations, we write down quantum transport equations (e.g. via the Keldysh formulation) for the quasiparticles and deduce a variety of transport properties. However, it has become clear in recent years that a number of interesting correlated electron materials do not fit easily into either of these paradigms. One promising and popular approach for describing these systems is to exploit their frequent proximity to quantum phase transitions [1], and so use a description in terms of "quantum criticality". This term refers to dynamics and transport in the non-zero temperature (T ) quantum critical region which spreads out from the T = 0 quantum critical point or phase (see Fig 2 below). Because there are no well-defined quasiparticles, and the excitations are strongly interacting, the description of quantum criticality is a challenging problem.It is useful to begin our discussion of quantum criticality by recalling a well-understood example of non-quasiparticle and non-order parameter dynamics: the Tomonaga-Luttinger (TL) liquid [2]. This is a compressible quantum state of many fermion or many bosons systems confined to move in one spatial dimension. Electronic quasiparticles are not well defined in

Absence of a quantum limit to charge diffusion in bad metals

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Shear viscosity of strongly interacting fermionic quantum fluids

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“…Similarly, we might expect that in the incoherent regime of transport, the shear viscosity η could violate the quantum limit to coherent transport, i.e., η < η q . Recently, a string theory based approach has been proposed to understand incoherent quantum transport in strongly correlated electron systems, especially the strange metal regime of doped cuprates [8][9][10][11][12]. The key idea of this method is to map a strongly coupled conformal field theory (CFT) to weakly coupled gravity in the anti-de Sitter (AdS) space in higher dimension [13].…”

Short-Lived Lattice Quasiparticles for Strongly Interacting Fluids

“…Under SIF conditions, most of the familiar and powerful notions of kinetic theory call for a profound revision. In particular, it is argued that not only Boltzmann's kinetic theory, but also the very notion of quasiparticles as weakly-interacting collective degrees of freedom, would lose meaning due their inconspicuously short lifetime [5]. Hence, new ideas and methods, both analytical and numerical, are in great demand.…”