Quantum critical dynamics for a prototype class of insulating antiferromagnets

Quantum criticality is a fundamental organizing principle for studying strongly correlated systems. Nevertheless, understanding quantum critical dynamics at nonzero temperatures is a major challenge of condensed matter physics due to the intricate interplay between quantum and thermal fluctuations. The recent experiments in the quantum spin dimer material TlCuCl$_3$ provide an unprecedented opportunity to test the theories of quantum criticality. We investigate the nonzero temperature quantum critical spin dynamics by employing an effective $O(N)$ field theory. The on-shell mass and the damping rate of quantum critical spin excitations as functions of temperature are calculated based on the renormalized coupling strength, which are in excellent agreements with experiment observations. Their $T\ln T$ dependence is predicted to be dominant at very low temperatures, which is to be tested in future experiments. Our work provides confidence that quantum criticality as a theoretical framework, being considered in so many different contexts of condensed matter physics and beyond, is indeed grounded in materials and experiments accurately. It is also expected to motivate further experimental investigations on the applicability of the field theory to related quantum critical systems.