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

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.

4+7 pages, 1+2 figs. v3: Paper simplified & reorganized to improve clarity. New appendix on analytic continuation. Minor corrections & added references

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• Dynamical response near quantum critical points
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• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
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• Spectral sum rules for conformal field theories in arbitrary dimensions
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