Constraining quantum critical dynamics: 2+1D Ising model and beyond

TL;DR

This paper derives non-perturbative constraints on the finite-temperature dynamics of quantum critical systems in 2+1 dimensions, providing universal sum rules and inequalities applicable to models like the QC Ising model.

Contribution

It establishes general non-perturbative constraints on the linear-response dynamics of conformal quantum critical systems at finite temperature in higher dimensions.

Findings

Derived sum rules for order parameter and scalar susceptibilities.

Established inequalities constraining dynamical shear viscosity.

Applied results to the 2+1D QC Ising model and related theories.

Abstract

Quantum critical (QC) phase transitions generally lead to the absence of quasiparticles. The resulting correlated quantum fluid, when thermally excited, displays rich universal dynamics. We establish non-perturbative constraints on the linear-response dynamics of conformal QC systems at finite temperature, in spatial dimensions above one. Specifically, we analyze the large frequency/momentum asymptotics of observables, which we use to derive powerful sum rules and inequalities. The general results are applied to the O(N) Wilson-Fisher fixed point, describing the QC Ising model when N = 1. We focus on the order parameter and scalar susceptibilities, and the dynamical shear viscosity. Connections to simulations, experiments and gauge theories are made.