A Holographic Model for Quantum Critical Responses

TL;DR

This paper develops a holographic model to analyze the dynamical conductivity of quantum critical states, revealing how it depends on model parameters and spectrum, and providing a framework for studying phase transitions.

Contribution

It introduces a self-consistent holographic model incorporating a scalar operator to study quantum critical responses and their dependence on parameters, including the spectrum and phase transition behavior.

Findings

Conductivity approximates Katz et al's ansatz across parameters.

Operator product expansion reveals the spectrum at high frequencies.

Framework aids in analytic continuation of quantum Monte Carlo data.

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.