Abstract
We consider the dynamics of paramagnons in 3D quantum antiferromagnets at nonzero temperature and in the vicinity of the quantum critical point. Upon approach to the phase transition, the heat bath causes infrared divergences in the paramagnon decay width calculated using standard perturbative approaches. 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. We obtain all results in the generic O(N) quantum field theory. Specifically we apply our results to TlCuCl\(_3\) (where we take \(N=3\)) and find compelling agreement with experimental data.
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For off-mass shell four momentum \(\mu ^2=\omega ^2-q^2\ne \Delta ^2\), the only significant contribution to Eq. (4.15) comes from the ‘window’ \(\mu ^2\approx \Delta ^2\pm \Gamma ^2\), since integrand (4.15) is heavily suppressed otherwise. In the limit \(\Delta \ll T\), \(\Gamma >\Delta \) but the running scale will be set by \(\Lambda =\max \{\mu ,T\}=T\). In the opposite limit \(\Delta \gg T\), then \(\Gamma \ll \Delta \) since \(\Gamma \sim e^{-\Delta /T}\) (see Sect. 4) and the running scale is essentially unaffected; \(\Lambda ^2\approx \Delta ^2\pm \Gamma ^2\approx \Delta ^2\)
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Scammell, H. (2018). A Nonperturbative Theory of Paramagnon Decay. In: Interplay of Quantum and Statistical Fluctuations in Critical Quantum Matter. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-97532-0_4
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DOI: https://doi.org/10.1007/978-3-319-97532-0_4
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