Quantum critical response: from conformal perturbation theory to holography

Abstract

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 non-perturbative sum rules. We show, via explicit computations, how holography recovers the general results of CFT, 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.

45+14 pages, 9 figures. v2: small clarifications, added references

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• Quantum Criticality
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Lifshitz holography: The whole shebang
• The quasi-normal modes of quantum criticality
• Optical conductivity of topological surface states with emergent supersymmetry
• Comments on Jacobson's "Entanglement equilibrium and the Einstein equation"
• Sum Rules from an Extra Dimension
• Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
• Critical capacitance and charge-vortex duality near the superfluid to insulator transition
• Constraining quantum critical dynamics: 2+1D Ising model and beyond

Cited by in corpus (16)

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• Holographic studies of Einsteinian cubic gravity
• Conformal correlators as simplex integrals in momentum space
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• Momentum space approach to crossing symmetric CFT correlators II: General spacetime dimension
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Holographic Butterfly Effect and Diffusion in Quantum Critical Region
• Momentum space CFT correlators for Hamiltonian truncation
• Unitarity and Universality in non relativistic Conformal Field theory
• Transport phenomena and Weyl correction in effective holographic theory of momentum dissipation
• Analytical study of the holographic superconductor from higher derivative theory
• Higher derivatives driven symmetry breaking in holographic superconductors
• Universal thermalization dynamics in (1+1)d QFTs