Dynamics and Conductivity Near Quantum Criticality

TL;DR

This paper investigates the dynamical properties and conductivity near quantum critical points in relativistic O(N) models in two dimensions, using Monte Carlo simulations and analytic continuation to reveal universal spectral features and critical conductivities.

Contribution

It provides detailed numerical analysis of spectral functions and conductivity across the quantum phase transition, including universal behaviors and a generalized worm algorithm for N>2.

Findings

Universal Higgs peak in scalar spectral function.

Confirmation of ^3 low-frequency rise for N=3,4.

Critical conductivity determined as ^*  0.3  0.1 in units of 4e^2/h.

Abstract

Relativistic O(N) field theories are studied near the quantum critical point in two space dimensions. We compute dynamical correlations by large scale Monte Carlo simulations and numerical analytic continuation. In the ordered side, the scalar spectral function exhibits a universal peak at the Higgs mass. For N=3 and 4 we confirm its \omega^3 rise at low frequency. On the disordered side, the spectral function exhibits a sharp gap. For N=2, the dynamical conductivity rises above a threshold at the Higgs mass (density gap), in the superfluid (Mott insulator) phase. For charged bosons, (Josephson arrays) the power law rise above the Higgs mass, increases from two to four. Approximate charge-vortex duality is reflected in the ratio of imaginary conductivities on either side of the transition. We determine the critical conductivity to be \sigma^*_c = 0.3 (\pm 0.1) 4e^2/h. In the appendices, we describe a generalization of the worm algorithm to N>2, and also a singular value decomposition error analysis for the numerical analytic continuation.