[Paper Review] Taking a critical look at holographic critical matter

D. V. Khveshchenko|arXiv (Cornell University)|Apr 28, 2014

Cosmology and Gravitation Theories3 citations

TL;DR

This paper critically evaluates the holographic approach to strongly correlated quantum matter, particularly non-Fermi liquid (NFL) states, by contrasting holographic predictions with conventional theoretical methods and experimental data. It advocates for systematic comparison across multiple observables—such as specific heat, conductivity, and susceptibility—to validate the approach, emphasizing that only by reproducing multiple universal scaling relations can holography claim predictive power beyond mere qualitative similarity.

ABSTRACT

Despite a recent flurry of applications of the broadly defined ('non-AdS/non-CFT') holographic correspondence to a variety of condensed matter problems, the status of this intriguing, yet speculative, approach remains largely undetermined. This note exposes a number of potential inconsistencies between the previously made holographic predictions and advocates for a compelling need to systematically contrast the latter against the results of alternate, more conventional, approaches as well as experimental data. It is also proposed to extend the list of computed observables and utilize the general relations between them as a further means of bringing the formal holographic approach into a closer contact with the physical realm.

Motivation & Objective

• To challenge the uncritical adoption of holographic duality in non-AdS/non-CFT contexts for condensed matter systems.
• To identify inconsistencies between holographic predictions and established theoretical or experimental results, particularly in transport and thermodynamic coefficients.
• To promote a systematic comparison of holographic results with those from conventional approaches like renormalization group, 1/N expansions, and functional integral methods.
• To extend the range of computed observables in holography beyond optical conductivity to include specific heat, magnetic susceptibility, and thermal conductivity.
• To establish that only by reproducing multiple universal scaling relations can holography be considered a robust framework for NFL states.

Proposed method

• Analyzing holographic predictions for thermodynamic and transport coefficients in theories dual to hyperscaling violating (HV) geometries using scaling theory.
• Applying the Kubo formula and the membrane paradigm to compute electrical conductivity, highlighting discrepancies between the two methods.
• Using the self-consistent equation for the self-energy: Σ(ω,q) = ∫ dε d^d p Λ²(ε)χ_E(ω+ε,p+q)G(ε,p), with G(ω,q) = (iω/Z − v·q)^−1.
• Deriving universal scaling exponents from the self-consistent solution: α = 1/2 − 1/z_b, ν = 1/(2 + z_b α), z_b = 4d/3, z_f = 1/(1−α).
• Evaluating observables via scaling: C ∼ T^{1−α}, σ ∼ ω^{α−1}, χ_s ∼ T^α, and comparing them with experimental data on YbRh2Si2 and CeCu6−xAux.
• Assessing the physical consistency of holographic models by testing their predictions against known universal relations and experimental benchmarks.

Experimental results

Research questions

• RQ1 Can the holographic approach consistently reproduce multiple universal scaling exponents across different observables in non-Fermi liquid states?
• RQ2 What are the inconsistencies between the Kubo formula and membrane paradigm predictions for electrical conductivity in holographic models?
• RQ3 How do holographic predictions for thermodynamic and transport coefficients compare with those from conventional field-theoretic methods?
• RQ4 To what extent do holographic models reproduce experimentally observed scaling behaviors in materials like YbRh2Si2 and CeCu6−xAux?
• RQ5 What role do general universal relations between observables play in validating the physical relevance of holographic models?

Key findings

• The holographic prediction for optical conductivity σ(ω) ∼ ω^{-2/3} in cuprates is not corroborated by later analysis and may be inconsistent with the more universal 1/ω scaling.
• The holographic approach often yields only simple scaling relations, suggesting simpler alternatives may achieve the same results with greater physical clarity.
• The self-consistent solution of the holographic self-energy equation produces scaling exponents that quantitatively match experimental data on YbRh2Si2 (d=3) and CeCu6−xAux (d=2).
• The derived scaling relations C ∼ T^{1−α}, σ ∼ ω^{α−1}, χ_s ∼ T^α are found to describe experimental data on NFL materials with high consistency.
• Discrepancies between the Kubo and membrane paradigm methods for conductivity highlight the need for careful physical interpretation of holographic results.
• The paper concludes that holography must reproduce multiple observables and universal relations to be considered a viable tool beyond speculative analogy.