A Holographic Model for Quantum Critical Responses

Abstract

We analyze the dynamical response functions of strongly interacting quantum critical states described by conformal field theories (CFTs). We construct a self-consistent holographic model that incorporates the relevant scalar operator driving the quantum critical phase transition. Focusing on the finite temperature dynamical conductivity $\sigma (\omega ,T)$, we study its dependence on our model parameters, notably the scaling dimension of the relevant operator. It is found that the conductivity is well-approximated by a simple ansatz proposed by Katz et al [1] for a wide range of parameters. We further dissect the conductivity at large frequencies $\omega >>T$ using the operator product expansion, and show how it reveals the spectrum of our model CFT. Our results provide a physically-constrained framework to study the analytic continuation of quantum Monte Carlo data, as we illustrate using the O(2) Wilson-Fisher CFT. Finally, we comment on the variation of the conductivity as we tune away from the quantum critical point, setting the stage for a comprehensive analysis of the phase diagram near the transition.

25+18 pages; 8+2 figures; 1 table. v3: published version

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Cited by in corpus (11)

• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• Conformal $n$-point functions in momentum space
• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• Thermal one point functions, large $d$ and interior geometry of black holes
• Thermal three-point functions from holographic Schwinger-Keldysh contours
• Holographic torus entanglement and its RG flow
• Transport phenomena and Weyl correction in effective holographic theory of momentum dissipation
• Holographic correlation functions at finite density and/or finite temperature
• Higher derivatives driven symmetry breaking in holographic superconductors
• A universal holographic prediction for quantum-critical dynamics