We develop a field-theoretic framework for work statistics in
O(N) models driven through criticality. By analyzing the dynamic renormalization group flow of composite power operators, we find the Kibble-Zurek scaling laws as a natural consequence of the flow, and we derive the scaling of work cumulants relevant to Kibble-Zurek scaling of topological defects from first principles, bypassing heuristic freeze-out argument. This yields the universal scaling
cn∼τQ−αn for the
n-th work cumulant density: isolated quantum systems exhibit a scaling of
αn=p(d+nz)ν/(1+pzν), whereas open quantum and classical systems undergo a dimensional collapse to
αn=pdν/(1+pzν). Validated by exact Gaussian solutions and numerical simulations, our theory establishes a foundation for general work statistics far from equilibrium, thereby bridging stochastic thermodynamics and the renormalization group theory.
A critically enhanced decay of the Loschmidt echo is characteristic of sudden quench dynamics near a quantum phase transition. Here, we demonstrate that the decay and revival of the Loschmidt echo follows power-law scaling in the system size and the distance from a critical point with equilibrium critical exponents. We reveal such dynamical scaling laws by analyzing relevant perturbations to the Loschmidt echo cast in a scaling invariant form. We confirm the validity and the generality of the predicted dynamical scaling laws with a diverse range of critical models such as Ising spin models with a short and long range interaction, a finite-component system phase transition, and a topological phase transition. Moreover, using the integrability of systems in the thermodynamic limit, we derive such scaling laws analytically from a microscopic analysis. Our finding promotes the Loschmidt echo to a quantitative non-equilibrium probe of criticality and allows for quantitative predictions on the role of criticality on various physical scenarios where the Loschmidt echo is central to describing non-equilibrium dynamics.
Abstract In finite systems singularities, such as discontinuities or divergences, associated with phase transitions are rounded. The extrapolation of finite size calculations to the singular thermodynamic limit makes use of scaling laws, introduced by Fisher, which involve the size of the system. The use and the theoretical basis of these laws are briefly reviewed here; some difficulties associated with the analytic calculation of the scaling functions are discussed. The correct treatment of zero‐momentum modes leads to a modified renormalization group picture; above the upper critical dimension (u.c.d.) finite size scaling does not hold but the properties of the finite system are easily calculable; below the u.c.d. the scaling functions are obtained in a systematic expansion in fractional powers of ϵ = 4–d. The rounding of first order transitions is also briefly considered; in spite of the lack of universality of the bulk transition itself, the rounding is universal because the correlation length of the finite system is large.