A holographic model for quantum critical responses

Myers, Robert C.; Sierens, Todd; Witczak-Krempa, William

doi:10.1007/jhep05(2016)073

Cited by 34 publications

(55 citation statements)

References 84 publications

(228 reference statements)

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“…In this paper, we will discuss the asymptotics of a variety of response functions at high frequency [5,8,[11][12][13][14][15][16][17][18][19][20]. We will show that in holographic field theories, this asymptotics is universal and does not depend in any detailed fashion on the nature of the ground state.…”

Section: Jhep07(2017)149mentioning

confidence: 97%

Quantum critical response: from conformal perturbation theory to holography

Lucas¹,

Sierens²,

Witczak-Krempa³

2017

J. High Energ. Phys.

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We discuss dynamical response functions near quantum critical points, allowing for both a finite temperature and detuning by a relevant operator. When the quantum critical point is described by a conformal field theory (CFT), conformal perturbation theory and the operator product expansion can be used to fix the first few leading terms at high frequencies. Knowledge of the high frequency response allows us then to derive nonperturbative sum rules. We show, via explicit computations, how holography recovers the general results of conformal field theory, and the associated sum rules, for any holographic field theory with a conformal UV completion -regardless of any possible new ordering and/or scaling physics in the IR. We numerically obtain holographic response functions at all frequencies, allowing us to probe the breakdown of the asymptotic high-frequency regime. Finally, we show that high frequency response functions in holographic Lifshitz theories are quite similar to their conformal counterparts, even though they are not strongly constrained by symmetry.

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Section: Jhep07(2017)149mentioning

confidence: 97%

Quantum critical response: from conformal perturbation theory to holography

Lucas¹,

Sierens²,

Witczak-Krempa³

2017

J. High Energ. Phys.

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“…[30][31][32][33][34] where an impressive agreement was found between the holographically computed frequency-dependent (finite-temperature) conductivity σ(ω) and the Monte Carlo results for the Bose-Hubbard model whose critical behaviour belongs to the universality class of the O(2)-symmetrical Wilson-Fisher critical point. Upon analytically continuing to the real frequencies this agreement gets progressively worse for ω < 2πT, though [86]. Most intriguingly, the original work of Refs.…”

Section: D+z-θmentioning

confidence: 93%

“…However, in the later Ref. [86] nearly identical results were obtained with the use of a much less exotic EMD model with U(ϕ) = ϕ 2 and V(ϕ) = 1 + αϕ. Thus, the previously reported agreement with the MC results (limited to ω > 2πT) appears to be rather common -an observation which takes away much of the intrigue surrounding the holographic model equipped with the term (14) and makes less pressing the need for understanding its otherwise inexplicably serendipitous success.…”

Section: D+z-θmentioning

confidence: 98%

“…Besides, it remains to be seen as to how the explicitly computed corrections to the optical conductivity of graphene [247][248][249][250][251][252][253] (38) match with the general prediction [86] , (39) where the sum is taken over the operator expansion of the product of two current operators. Another quantity of special interest would be the Lorenz ratio (ordinary, as well as the Hall one) as a function of frequency.…”

Section: Holographic Transport: Dirac/weyl Materialsmentioning

confidence: 98%

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Demystifying the holographic mystique: A critical review

Khveshchenko¹

2016

Lith. J. Phys.

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Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).Keywords: strongly correlated systems, holographic correspondence, transport theory, strange metals, analogue gravity PACS: 71.27.+a Condensed matter holography: the promiseAmong the outstanding grand problems in condensed matter physics is that of a deeper understanding and classification of the so-called 'strange metals' or compressible non-Fermi liquid (NFL) states of the strongly interacting systems. However, despite all the effort and a plethora of the important and nontrivial results obtained with the use of the traditional techniques, this program still remains far from completion.As an alternate approach, over the past decade there have been numerous attempts inspired by the hypothetical idea of holographic correspondence which originated from string/gravity/high energy theory (where it is known under the acronym AdS/ CFT) to adapt its main concepts to various condensed matter (or, even more generally, quantum manybody) systems at finite densities and temperatures [1][2][3][4][5][6][7].In its original context, the bona fide holographic principle postulates that certain d + 1-dimensional ('boundary') quantum field theories (e. g. the maximally supersymmetric SU(N) gauge theory) may allow for a dual description in terms of a string theory which, upon a proper compactification, amounts to a certain d + 2-dimensional ('bulk') supergravity. Moreover, in the strong coupling limit (characterized in terms of the t'Hooft coupling constant λ = g 2 N >> 1) and for a large rank N > > 1 of the gauge symmetry group, the bulk description can be further reduced down to a weakly fluctuating gravity model which can even be treated semiclassically at the lowest (0th) order of the underlying 1/N-expansion.In the practical applications of the holographic conjecture, the partition function of a strongly interacting boundary theory with the Lagrangian L(ϕ a ) would then be approximated by a saddle-point (classical) value of the bulk action described by the Lagrangian L(g μν ,…) which includes gravity and other fields dual to their boundary counterparts [1][2][3][4][5][6][7][8] (1) evaluated with the use of a fixed background metric ,while any quantum corrections would usually be neglected by invoking the small parameter 1/N.

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“…Sum rules are analytic structures that are used to constrain spectral densities of any quantum field theory [1][2][3][4][5][6][7][8]. Schematically they are weighted moments of the spectral density over frequency, which are proportional to one point functions in the theory.…”

Section: Introductionmentioning

confidence: 99%

Shear sum rule in higher derivative gravity theories

Chowdhury

2017

J. High Energ. Phys.

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We study holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum rules relate weighted integral over spectral densities of retarded correlators in the shear channel to the one point functions of the CFTs. The proportionality constant can be written in terms of the data of three point functions of the stress tensors of the CFT (t 2 and t 4 ). For CFTs dual to two derivative Einstein gravity, this proportionality constant is just d 2(d+1) . This has been verified by a direct holographic computation of the retarded correlator for Einstein gravity in AdS d+1 black hole background. We compute corrections to the holographic shear sum rule in presence of higher derivative corrections to the Einstein-Hilbert action. We find agreement between the sum rule obtained from a general CFT analysis and holographic computation for Gauss Bonnet theories in AdS 5 black hole background. We then generalize the sum rule for arbitrary curvature squared corrections to Einstein-Hilbert action in d ≥ 4. Evaluating the parameters t 2 and t 4 for the possible dual CFT in presence of such curvature corrections, we find an agreement with the general field theory derivation to leading order in coupling constants of the higher derivative terms.

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A holographic model for quantum critical responses

Cited by 34 publications

References 84 publications

Quantum critical response: from conformal perturbation theory to holography

Quantum critical response: from conformal perturbation theory to holography

Demystifying the holographic mystique: A critical review

Shear sum rule in higher derivative gravity theories

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