Non-equilibrium quantum mechanics: A 'hot quantum soup' of paramagnons

TL;DR

This paper develops a quantum kinetic theory for paramagnon decay in quantum antiferromagnets near criticality, revealing a new 'hot quantum soup' regime where decay width rivals energy, with applications to TlCuCl3.

Contribution

It introduces a novel finite frequency, finite temperature technique for nonlinear quantum field theory applicable near quantum critical points.

Findings

Agreement with experimental data for TlCuCl3

Identification of the 'hot quantum soup' regime near Neel temperature

Logarithmic running of coupling constants alters traditional phase regime views

Abstract

Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet TlCuCl3, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a non-perturbative, 'hot quantum soup' regime where paramagnon width is comparable to its energy; (ii) usual perturbative regime where paramagnon width is significantly lower than its energy. Close to the Neel tempera- ture the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the 'golden rule of quantum kinetics'. The formulation is generic and applicable to any three dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically we apply our results to TlCuCl3 and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.