The Dynamics of Quantum Criticality Revealed by Quantum Monte Carlo and Holography

Abstract

Understanding the dynamics of quantum systems without long-lived excitations (quasiparticles) constitutes an important yet challenging problem. Although numerical techniques can yield results for the dynamics in imaginary time, their reliable continuation to real time has proved difficult. We tackle this issue using the superfluid–insulator quantum critical point of bosons on a two-dimensional lattice, where quantum fluctuations destroy quasiparticles. We present quantum Monte Carlo simulations for two separate lattice realizations. Their low-frequency conductivities turn out to have the same universal dependence on imaginary frequency and temperature. Using the structure of the real-time dynamics of conformal field theories described by the holographic gauge/gravity duality, we then make progress on the problem of analytically continuing the numerical data to real time. Our method yields quantitative and experimentally testable results on the frequency-dependent conductivity near the quantum critical point. Extensions to other observables and universality classes are discussed.