Gravity dual of a quantum Hall plateau transition

Davis, Joshua L.; Kraus, Per; Shah, Amit P.

doi:10.1088/1126-6708/2008/11/020

Cited by 89 publications

(107 citation statements)

References 120 publications

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“…Using the now standard Karch-O'Bannon technique [17,18], we can compute the currents by requiring reality of the action or the equations of motion (see also [5]). As before, the details can be found in Appendix C. In particular, the quantity X(r) in (53) must be non-negative.…”

Section: Conductivitiesmentioning

confidence: 99%

“…This is simply a manifestation of the repulsive interaction between the two kinds of branes in flat space. Nevertheless, some aspects of the quantum Hall effect have been modeled in this system by considering the D7-brane embedding in the asymptotically flat, rather than near-horizon, D3-brane background and varying the mass of the fermion rather than the magnetic field, which gives a toy model for a plateau transition [5]. This D3-D7 setup has also been used to study some aspects of large N three-dimensional QCD in [6].…”

Section: Introductionmentioning

confidence: 99%

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Quantum Hall effect in a holographic model

Bergman¹,

Jokela²,

Lifschytz³

et al. 2010

J. High Energ. Phys.

163

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We consider a holographic description of a system of strongly coupled fermions in 2 + 1 dimensions based on a D7-brane probe in the background of D3-branes, and construct stable embeddings by turning on worldvolume fluxes. We study the system at finite temperature and charge density, and in the presence of a background magnetic field. We show that Minkowski-like embeddings that terminate above the horizon describe a family of quantum Hall states with filling fractions that are parameterized by a single discrete parameter. The quantization of the Hall conductivity is a direct consequence of the topological quantization of the fluxes. When the magnetic field is varied relative to the charge density away from these discrete filling fractions, the embeddings deform continuously into black-hole-like embeddings that enter the horizon and that describe metallic states. We also study the thermodynamics of this system and show that there is a first order phase transition at a critical temperature from the quantum Hall state to the metallic state.

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Section: Conductivitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Hall effect in a holographic model

Bergman¹,

Jokela²,

Lifschytz³

et al. 2010

J. High Energ. Phys.

163

View full text Add to dashboard Cite

show abstract

“…Extensions which break parity and time-reversal, of relevance to the quantum Hall effect, have also been studied [47,48].…”

Section: Recent Developmentsmentioning

confidence: 99%

Quantum criticality and black holes

Sachdev

Müller

2009

J. Phys.: Condens. Matter

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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

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“…The Ind (D) is a powerful topological quantity that has been used for diverse purposes [3]- [14]; see also [15] and refs therein for other applications; it gives a rigorous explanation of the origin of chiral anomalies and constitutes an alternative approach to the perturbative method based on computing radiative corrections to describeΨγ µ ΨA µ interactions in QFT 1+2 where the topological Chern-Simons gauge theory emerges as a 1-loop correction of the gauge field propagator [16,17]. In 2-dimensions, the computation of Ind (D) shows that the anomalous quantum Hall effect (QHE) of graphene [18][19][20] is precisely due to the chiral anomaly of zero modes; a basic result that is expected to be valid as well for higher dimensional Dirac fermions in background fields including light quarks on 4D hyperdiamond [21]- [28] and fermions on higher 2N-dimensional honeycombs.…”

Section: Introductionmentioning

confidence: 99%

Topological aspects of fermions on hyperdiamond

Saidi¹,

Fassi-Fehri²,

Bousmina³

2012

Journal of Mathematical Physics

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Motivated by recent results on the index of the Dirac operator D = γ µ D µ of QCD on lattice and also by results on topological features of electrons and holes of 2-dimensional graphene, we compute in this paper the Index of D for fermions living on a family of even dimensional lattices denoted as L 2N and describing the 2N-dimensional generalization of the graphene honeycomb. The calculation of this topological Index is done by using the direct method based on solving explicitly the gauged Dirac equation and also by using specific properties of the lattices L 2N which are shown to be intimately linked with the weight lattices of SU (2N + 1). The Index associated with the two leading N = 1 and N = 2 elements of this family describe precisely the chiral anomalies of graphene and QCD 4 . Comments on the method using the spectral flow approach as well as the computation of the topological charges on 2-cycles of 2N-dimensional compact supercell in L 2N and applications to QCD 4 are also given.

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Gravity dual of a quantum Hall plateau transition

Cited by 89 publications

References 120 publications

Quantum Hall effect in a holographic model

Quantum Hall effect in a holographic model

Quantum criticality and black holes

Topological aspects of fermions on hyperdiamond

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