We explore the fundamental limits on finite-time driving in quantum critical systems described by boundary conformal field theory. We show that stochastic work fluctuations arising from external driving are a resource for speedy control, and derive an exact, saturable fluctuation-based speed limit in weakly driven boundary conformal field theories at finite temperature. The bound and saturating protocol can be expressed entirely in terms of the universal scaling dimension, and the result interpolates between the Kibble--Zurek regime,where temporal correlations are strongly nonlocal, and an adiabatic regime where linear driving becomes optimal. For small scaling dimension, the enhanced temporal correlations produce pronounced departures from linear protocols and a larger optimization advantage. These results establish a universal work precision--time tradeoff for boundary-critical control, applicable to quantum impurity, fractional quantum Hall, and superconducting-circuit platforms.
We explore the fundamental limits on finite-time driving in quantum critical systems described by boundary conformal field theory. We show that stochastic work fluctuations arising from external driving are a resource for speedy control, and derive an exact, saturable fluctuation-based speed limit in weakly driven boundary conformal field theories at finite temperature. The bound and saturating protocol can be expressed entirely in terms of the universal scaling dimension, and the result interpolates between the Kibble--Zurek regime,where temporal correlations are strongly nonlocal, and an adiabatic regime where linear driving becomes optimal. For small scaling dimension, the enhanced temporal correlations produce pronounced departures from linear protocols and a larger optimization advantage. These results establish a universal work precision--time tradeoff for boundary-critical control, applicable to quantum impurity, fractional quantum Hall, and superconducting-circuit platforms.
A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes, depending on the drive frequency. We compute the behavior of quantities including the entanglement entropy and Loschmidt echo, confirming analytic predictions from field theory by exact numerics on the transverse field Ising model and demonstrate universality by adding nonintegrable perturbations. The dynamics naturally separate into three regimes: a slow-driving limit, which has an interpretation as multiple quantum quenches with amplitude corrections from CFT; a fast-driving limit, in which the system behaves as though subject to a single quantum quench; and a crossover regime displaying heating. The universal Floquet dynamics in all regimes can be understood using a combination of boundary CFT and Kibble-Zurek scaling arguments.
The Kibble-Zurek mechanism (KZM) and finite-time scaling (FTS) provide a foundational framework for driven critical dynamics, yet their predictive power has been largely confined to local observables. Here, we establish a universal finite-time scaling theory for the nonequilibrium dynamics of quantum entanglement. Using unbiased quantum Monte Carlo simulations, we investigate the corner entanglement entropy of (2+1)-dimensional interacting Dirac fermions driven from ordered phases toward a quantum critical point. We find that the corner entanglement accurately obeys a universal driven scaling governed by the driving rate and system size, persisting whether the initial ordered state is fully gapped or hosts gapless Goldstone modes. Crucially, this dynamical entanglement exhibits a logarithmic dependence on the driving rate, from which the universal corner coefficient of the underlying conformal field theory can be robustly extracted far from equilibrium. These results generalize the KZM from local observables to the intrinsic nonlocal quantum information measures, offering a practical blueprint for characterizing quantum criticality and entanglement on programmable quantum simulators.
The celebrated Kibble-Zurek mechanism (KZM) describes the scaling of physical quantities when external parameters sweep through a critical point. Boundaries are ubiquitous in real systems, and critical behaviors near the boundary have attracted extensive research. Different boundary universality classes, including ordinary, special, extraordinary, and surface transitions, have been identified. However, the driven critical dynamics near boundaries remains unexplored. Here, we systematically investigate the driven critical dynamics in various boundary universality classes of the Ising model in both two and three dimensions, and discover a wealth of dynamic scaling behaviors. We find that for heating dynamics in all boundary universality classes, as well as for cooling dynamics in special, extraordinary, and surface transitions, the dynamic scaling behaviors of the order parameter can be described by a normal generalization of the KZM, called boundary finite-time scaling (BFTS). In contrast, for cooling dynamics in ordinary transition, we discover an abnormal logarithmic scaling on the driving rate. Moreover, for the special transition, in addition to temperature driving, we also consider the driven dynamics by driving the surface couplings. For increasing the surface coupling across the special transition point along the line of the ordinary transition, the prerequisite of the KZM, which requires that the correlation length/time in the initial state to be short-ranged, breaks down. We develop a generalized BFTS for a nonequilibrium initial state characterized by the waiting time, or the ``age'', of the boundary. Possible generalizations are also discussed.
The pursuit of a universal description for nonequilibrium critical dynamics in quantum many-body systems stands as a central frontier in modern statistical physics. For driven critical dynamics starting far from the critical point, the well-known Kibble-Zurek (KZ) scaling holds only when the driving rate lies below an upper bound. Here we study driven dynamics restricted to the critical region, and show that robust dynamic scaling behavior exists for arbitrary driving rates. We develop a generalized finite-time scaling (FTS) framework, which provides a unified understanding on the driven dynamics for the full range of quench rates, bridging the KZ scaling in the slow-driving regime and the De~Grandi-Gritsev-Polkovnikov (DGP) scaling in the sudden-quench limit. We verify this unified FTS form through numerical simulations in both quantum critical and tricritical points. The good agreement between theoretical predictions and numerical results confirms the generality of our theory. Our work establishes a universal theory for nonequilibrium critical dynamics spanning the full range of driving rates, with broad implications for quantum quench experiments and out-of-equilibrium statistical mechanics.
We derive the finite-temperature characteristic function of work (CFW) for a driven O(N) Gaussian field theory and obtain closed-form expressions for all zero-temperature excess-work cumulants. For gapped protocols, we use adiabatic perturbation theory (APT) to derive the τQ−2 scaling for protocols with a nonzero first derivative at either boundary, where τQ is the protocol duration; smoother boundaries lead to faster decay. For power-law protocols approaching the critical point with exponent p, we determine the competition between critical excitations and the regular contribution. The nth cumulant's critical contribution follows Kibble--Zurek (KZ) scaling τQ−p(d+n)/(p+2) for d+n<2p+4, acquires a logarithmic correction τQ−2plogτQ at d+n=2p+4, and scales as τQ−2p above this condition, where d is the spatial dimension. This analytical study of the APT--KZ crossover in a solvable model provides a basis for studying their competition in interacting field theories.
When an external parameter drives a system across a quantum phase transition at a finite rate, work is performed on the system and entropy is dissipated, due to creation of excitations via the Kibble-Zurek mechanism. Although both the adiabatic and sudden-quench limits have been studied in detail, the quantum work statistics along the crossover connecting these limits has largely been an open question. Here, we obtain exact scaling functions for the work statistics along the full crossover from adiabatic to sudden-quench limits for critical quantum impurity problems, by combining linear response theory, conformal field theory, and the numerical renormalization group. These predictions can be tested in charge-multichannel Kondo quantum dot devices, where the dissipated work corresponds to the creation of nontrivial excitations such as Majorana fermions or Fibonacci anyons.