This work discusses the effects of many-body interactions on the statistics of work in inhomogeneous fermionic chains driven for finite times and across the precursor to the metal-Mott insulator quantum phase transition. For dynamics beyond sudden quenches, a change in sign and a variation in value of the skewness signal the transition, while entropy production dominates work fluctuations even for slow processes, in contrast to the classical work fluctuation dissipation relation.
This work discusses the effects of many-body interactions on the statistics of work in inhomogeneous fermionic chains driven for finite times and across the precursor to the metal-Mott insulator quantum phase transition. For dynamics beyond sudden quenches, a change in sign and a variation in value of the skewness signal the transition, while entropy production dominates work fluctuations even for slow processes, in contrast to the classical work fluctuation dissipation relation.
The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of the system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a nonequilibrium dynamics. By driving transient currents to oppose the precursor to the metal-Mott-insulator transition in a diversity of dynamical regimes, we show how increasing many-body interactions dramatically affect the statistics of energy fluctuations and, consequently, the extractable work distribution of finite Hubbard chains. Statistical properties of such distributions as its skewness with its impressive change across the transition can be related to irreversibility and entropy production. Even for slow driving rates, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong features in the work distribution. In the Mott-insulating phase, the work fluctuation-dissipation balance gets modified with the irreversible entropy production dominating over work fluctuations. Because of this, effects of an interaction-driven quantum phase transition on thermodynamic quantities and irreversibility must be considered in the design of protocols in small-scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols on a quantum scale.
Entanglement in many-body systems may display interesting signatures of quantum phase transitions and similar properties are starting to be encountered in the analysis of work fluctuations. Here, we consider the fermionic superfluid-to-insulator transition (SIT) and relate its entanglement properties with its work distribution statistics. The SIT is modeled by the attractive fermionic Hubbard model in the presence of randomly distributed impurities. The work distribution is calculated across two quench protocols, both triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. Our results indicate that, the critical state that induces minimization of the entanglement also maximizes the average work. We demonstrate that, for this state, density fluctuations vanish at all orders, hence all central moments of the work probability distribution are exactly zero at criticality. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal result. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature could be used to implement a quantum critical battery. The effects of temperature on these signatures of critical behaviour are also investigated and shown to favor work extraction for high enough temperatures.
We study properties of the work distribution of a many-body system driven through a quantum phase transition in finite time. We focus on the non-Gaussianity of the distribution, which we characterize through two quantitative metrics: skewness and negentropy. In particular, we focus on the quantum Ising model and show that a finite duration of the ramp enhances the non-Gaussianity of the distribution for a finite size system. By examining the characteristics of the full distribution, we observe that there is a clear intermediate regime between the sudden quench and adiabatic limits, where the distribution becomes increasingly skewed.
Abstract Understanding the dynamical consequences of quantum phase transitions on thermodynamical quantities, such as work statistics and entropy production, is one of the most intriguing aspect of quantum many-body systems, pinpointing the emergence of irreversibility to critical features. In this work, we investigate the critical fingerprints appearing in these key thermodynamical quantities for a mean-field critical system undergoing a finite-time cycle, starting from a thermal state at a generic inverse temperature. In contrast to non-zero dimensional many-body systems, the presence of a mean-field critical point in a finite-time cycle leads to constant irreversible work even in the limit of infinitely slow driving. This links with the fact that a slow finite-time cycle results in a constant amount of squeezing, which enables us to derive analytical expressions for the work statistics and irreversible entropy, depending solely on the mean-field critical exponents and the functional form of the control parameter near the critical point. We find that the probability of observing negative work values, corresponding to negative irreversible entropy, is inversely proportional to the time the system remains near to the critical point, and this trend becomes less pronounced the lower the temperature of the initial thermal state. Finally, we determine the irreversibility traits under squeezing generation at zero-temperature using the relative entropy of coherence.
We study three aspects of work statistics in the context of the fluctuation theorem for quantum spin chains up to 1024 sites by numerical methods based on matrix-product states (MPSs). First, we use our numerical method to evaluate the moments/cumulants of work done by the sudden quench process on the Ising or Haldane spin chains, and we study their behaviors across the quantum phase transitions. Our results show that, up to the fourth cumulant, the work statistics can indicate the quantum phase transition characterized by the local order parameters but barely for purely topological phase transitions. Second, we propose to use the fluctuation theorem, such as Jarzynski's equality, which relates the real-time correlator to the ratio of the thermal partition functions, as a benchmark indicator for the numerical real-time evolving methods. Third, we study the passivity of ground and thermal states of quantum spin chains under some cyclic impulse processes. We show that the passivity of thermal states and ground states under the Hermitian actions is ensured by the second laws and variational principles, respectively, and we also verify this by numerical calculations. In addition, we also consider the passivity of ground states under non-Hermitian actions, for which the variational principle cannot be applied. Despite that, we find no violation of passivity from our numerical results for all the cases considered in the Ising and Haldane chains. Overall, we demonstrate that the work statistics for the sudden quench and impulse processes can be evaluated precisely by the numerical MPS method to characterize quantum phase transitions and examine the passivity of quantum states. We also propose to exploit the universality of the fluctuation theorem to benchmark the numerical real-time evolutions in an algorithmic and model-independent way. Published by the American Physical Society 2024
Abstract Entanglement in many‐body systems may display quantum phase transition signatures, and analogous insights are emerging in the study of work fluctuations. Here, the fermionic superfluid‐to‐insulator transition (SIT) is considered and related to its entanglement properties and its work distribution statistics. Using the attractive fermionic Hubbard model with randomly distributed impurities, the work distribution is analyzed under two quench protocols triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. The results indicate that, at criticality, the entanglement is minimized while the average work is maximized. This study demonstrates that, for this state, density fluctuations vanish at all orders, resulting in all central moments of the work probability distribution being precisely zero. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal results. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature can be used to implement a quantum critical battery. The impact of temperature on this critical behaviour is also investigated and shown to favor work extraction for high enough temperatures.