Dynamical response near quantum critical points

Abstract

We study high frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz invariance, powerful methods from conformal field theory allow us to fix the high frequency response in terms of universal coefficients. We test our predictions analytically in the large-N O(N) model and using the gauge-gravity duality, and numerically via Quantum Monte Carlo simulations on a lattice model hosting the interacting superfluid-insulator QCP. In superfluid phases, interacting Goldstone bosons qualitatively change the high frequency optical conductivity, and the corresponding sum rule.

4+12 pages. 2+2 figures. v2: Added explanations throughout, and new results in Appendix C for the ordered phase. Published version

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• Designer Monte Carlo Simulation for Gross-Neveu Transition
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• Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions
• Holographic response from higher derivatives with homogeneous disorder
• Unitarity and Universality in non relativistic Conformal Field theory
• Superuniversal transport near a $(2+1)$-dimensional quantum critical point
• Strong terahertz third-harmonic generation by kinetic heavy quasiparticles in CaRuO${}_3$
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