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

References in corpus (8)

• Quantum Criticality in Heavy Fermion Metals
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• The quasi-normal modes of quantum criticality
• 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 (5)

• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• Quantum spin chains with multiple dynamics
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Holographic response from higher derivatives with homogeneous disorder
• Momentum dissipation and holographic transport without self-duality