Dynamical response near quantum critical points

TL;DR

This paper investigates the high-frequency optical conductivity near quantum critical points, incorporating effects of detuning and temperature, and employs various theoretical and numerical methods to understand universal response behaviors.

Contribution

It provides a unified framework for high-frequency responses near QCPs, utilizing conformal field theory, large-N models, gauge-gravity duality, and Quantum Monte Carlo simulations.

Findings

Universal high-frequency response fixed by conformal symmetry

Goldstone bosons significantly alter optical conductivity in superfluid phases

Sum rules are clarified and validated across different models

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.