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We investigate the efficiency of approximate counterdiabatic driving (CD) in accelerating adiabatic passage through a first-order quantum phase transition. Specifically, we analyze a minimal spin-glass bottleneck model that is analytically tractable and exhibits both an exponentially small gap at the transition point and a change in the ground state that involves a macroscopic rearrangement of spins. Using the variational Floquet-Krylov expansion to construct CD terms, we find that while the formation of excitations is significantly suppressed, achieving fully adiabatic evolution remains challenging, necessitating high-order nonlocal terms in the expansion. Our results demonstrate that local CD strategies have limited effectiveness when crossing the extremely small gaps characteristic of NP-hard Ising problems. To address this limitation, we propose an alternative method, termed quantum brachistochrone counterdiabatic driving (QBCD), which significantly increases the fidelity to the target state over the expansion method by directly addressing the gap-closing point and the associated edge states.

We consider the optimal driving of the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf's local adiabatic driving and the quantum adiabatic brachistochrone, fail to provide a significant speedup over the adiabatic evolution in the transverse-field Ising and long-range Kitaev models. As an alternative, we introduce a novel framework, Non-Adiabatic Quantum Optimization (NAQO), that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. NAQO is not restricted to exactly solvable models, and we further confirm its superior performance in a disordered non-integrable model., Comment: 24 pages, 15 figures, comments welcome

The spin-vector Monte Carlo model is widely used as a benchmark for the classicality of quantum annealers but severely restricts the time evolution. The spin-vector Langevin (SVL) model has been proposed and tested as an alternative, closely reproducing the real-time dynamics of physical quantum annealers such as D-Wave machines in the dissipative regime. We investigate the SVL annealing dynamics of classical O(2) rotors on regular graphs, identifying universal features in the nonequilibrium dynamics when changing the range of interactions and the topology of the graph. Regular graphs with low connectance or edge density exhibit universal scaling dynamics consistent with the Kibble-Zurek mechanism, which leads to a power-law dependence of the density of defects and the residual energy as a function of the annealing time. As the interaction range is increased, the power-law scaling is suppressed, and an exponential scaling with the annealing time sets in. Our results establish a universal breakdown of the Kibble-Zurek mechanism in classical systems characterized by long-range interactions, in sharp contrast with previous findings in the quantum domain.

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the $AdS/CFT$ correspondence by solving the Einstein-Abelian-Higgs model in an $AdS_4$ black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter., Comment: 13 pages, 7 figures

We report a systematic investigation of universal quantum chaotic signatures in the transverse field Ising model on an Erd\H{o}s-R\'enyi network. This is achieved by studying local spectral measures such as the level spacing and the level velocity statistics. A spectral form factor analysis is also performed as a global measure, probing energy level correlations at arbitrary spectral distances. Our findings show that these measures capture the breakdown of chaotic behavior upon varying the connectivity and strength of the transverse field in various regimes. We demonstrate that the level spacing statistics and the spectral form factor signal this breakdown for sparsely and densely connected networks. The velocity statistics capture the surviving chaotic signatures in the sparse limit. However, these integrable-like regimes extend over a vanishingly small segment in the full range of connectivity.

We investigate numerically how onsite disorder affects conduction in the periodically driven Rice-Mele model, a prototypical realization of the Thouless pump. Although the pump is robust against disorder in the fully adiabatic limit, much less is known about the case of finite period time $T$, which is relevant also in light of recent experimental realizations. We find that at any fixed period time and nonzero disorder, increasing the system size $L\to\infty$ always leads to a breakdown of the pump, indicating Anderson localization of the Floquet states. Our numerics indicate, however, that in a properly defined thermodynamic limit, where $L/T^\theta$ is kept constant, Anderson localization can be avoided, and the charge pumped per cycle has a well-defined value -- as long as the disorder is not too strong. The critical exponent $\theta$ is not universal, rather, its value depends on the disorder strength. Our findings are relevant for practical, experimental realizations of the Thouless pump, for studies investigating the nature of its current-carrying Floquet eigenstates, as well as the mechanism of the full breakdown of the pump, expected if the disorder exceeds a critical value., Comment: 5+5 pages, 4+6 figures

The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the first model the external drivings are realized by a continuous variation of the on-site energies, in the second one it is generated by deformations of a parabolic potential. We concentrate on the effects of the potential on the localization properties and investigate the statistics of the energy level velocities and curvatures regarding their typical magnitudes and domain of agreement with the predictions of Random Matrix Theory (RMT) for the Gaussian Orthogonal, Unitary and Symplectic ensembles. Moreover, the statistical properties of the avoided level crossings are investigated in terms of the corresponding Landau-Zener parameters. We find that the strength of the Landau-Zener transitions exhibits universal behavior which also implies universal single-particle dynamics for slow perturbations independent of the disorder and potential strength, the system size and the symmetry class. These results can be verified experimentally by measurements of single-particle energy spectra in quantum dots., Comment: 11 pages, 6 figures

We study the full distribution of quantum work in generic, noninteracting, disordered fermionic nanosystems at finite temperature. We derive an analytical determinant formula for the characteristic function of work statistics for quantum quenches starting from a thermal initial state. For work small compared to the thermal energy of the Fermi gas, work distribution is Gaussian, and the variance of work is proportional to the average work, while in the low temperature or large work limit, a non-Gaussian distribution with superdiffusive work fluctuations is observed. Similarly, the time dependence of the probability of adiabaticity crosses over from an exponential to a stretched exponential behavior. For large enough average work, the work distribution becomes universal, and depends only on the temperature and the mean work. Apart from initial low temperature transients, work statistics are well captured by a Markovian energy-space diffusion process of hard-core particles, starting from a thermal initial state. Our findings can be verified by measurements on nanoscale circuits or via single qubit interferometry., Comment: 12+8 pages, 7+1 figures

We present a theory of quantum work statistics in generic chaotic, disordered Fermi liquid systems within a driven random matrix formalism. By extending P. W. Anderson's orthogonality determinant formula to compute quantum work distribution, we find that work statistics is non-Gaussian and is characterized by a few dimensionless parameters. At longer times, quantum interference effects become irrelevant and the quantum work distribution is well-described in terms of a purely classical ladder model with a symmetric exclusion process in energy space, while bosonization and mean field methods provide accurate analytical expressions for the work statistics. Our random matrix and mean field predictions are validated by numerical simulations for a two-dimensional disordered quantum dot, and can be verified by calorimetric measurements on nanoscale circuits., Comment: 5+5 pages, 3+2 figures

We generalize Anderson's orthogonality determinant formula to describe the statistics of work performed on generic disordered, non-interacting fermionic nanograins during quantum quenches. The energy absorbed increases linearly with time, while its variance exhibits a superdiffusive behavior due to Pauli's exclusion principle. The probability of adiabatic evolution decays as a stretched exponential. In slowly driven systems, work statistics exhibits universal features, and can be understood in terms of fermion diffusion in energy space, generated by Landau-Zener transitions. This diffusion is very well captured by a Markovian symmetrical exclusion process, with the diffusion constant identified as the energy absorption rate. The energy absorption rate shows an anomalous frequency dependence at small energies, reflecting the symmetry class of the underlying Hamiltonian. Our predictions can be experimentally verified by calorimetric measurements performed on nanoscale circuits., Comment: 10 pages, 8 figures (including appendix), accepted version, extended main text