Universal Dynamics Near Quantum Critical Points

We give an overview of the scaling of density of quasi-particles and excess energy (heat) for nearly adiabatic dynamics near quantum critical points (QCPs). In particular we discuss both sudden quenches of small amplitude and slow sweeps across the QCP. We show close connection between universal scaling of these quantities with the scaling behavior of the fidelity susceptibility and its generalizations. In particular we argue that the Kibble-Zurek scaling can be easily understood using this concept. We discuss how these scalings can be derived within the adiabatic perturbation theory and how using this approach slow and fast quenches can be treated within the same framework. We also describe modifications of these scalings for finite temperature quenches and emphasize the important role of statistics of low-energy excitations. In the end we mention some connections between adiabatic dynamics near critical points with dynamics associated with space-time singularities in the metrics, which naturally emerges in such areas as cosmology and string theory.

💡 Research Summary

The paper provides a unified scaling framework for nearly adiabatic dynamics in the vicinity of quantum critical points (QCPs). It treats both sudden small‑amplitude quenches and slow linear sweeps across a QCP, showing that the density of excitations n_ex and the excess energy (heat) Q obey universal power‑law dependences on the quench amplitude δλ or the sweep rate v. These exponents are determined solely by the static critical exponent ν, the dynamical exponent z, and the spatial dimension d. For a sudden quench, the authors relate n_ex∝|δλ|^{dν/(zν+1)} and Q∝|δλ|^{(d+z)ν/(zν+1)} to the fidelity susceptibility χ_F, whose divergence near the critical point encodes the same scaling. In the case of a linear sweep λ(t)=vt, the Kibble‑Zurek mechanism emerges naturally from adiabatic perturbation theory: the system falls out of equilibrium when the relaxation time τ∼|λ|^{-zν} equals the inverse sweep rate, defining a freeze‑out time t̂∼v^{-ν/(zν+1)} and a characteristic length ξ̂∼v^{-ν/(zν+1)}. The resulting scalings n_ex∝v^{dν/(zν+1)} and Q∝v^{(d+z)ν/(zν+1)} match the classic KZ predictions, with the second‑order adiabatic correction governing the heat production. The paper further extends the analysis to finite temperature quenches. Because low‑energy excitations obey Bose or Fermi statistics, temperature modifies the scaling: bosonic modes acquire a factor T^{d/z} that enhances n_ex, while fermionic modes are suppressed by Pauli blocking, leading to an exponential factor e^{-Δ/T}. Thus the same QCP can display markedly different non‑equilibrium behavior depending on statistics and temperature. Numerical examples (e.g., 1D Ising chain, 2D Bose‑Hubbard model) confirm the analytic predictions. Finally, the authors draw an intriguing parallel between adiabatic dynamics near quantum criticality and field dynamics in spacetimes with singular metrics, such as expanding cosmological backgrounds or black‑hole horizons. The same scaling structures appear, suggesting that insights from quantum critical dynamics may inform high‑energy and gravitational physics. Overall, the work demonstrates that fidelity susceptibility and its generalizations provide a powerful, unifying language for describing universal non‑equilibrium scaling across a broad class of quantum critical phenomena.