Scaling of quantum work distribution for interacting many-body systems

Understanding the dynamics small quantum systems out-of-equilibrium is at
the core of quantum thermodynamics and its application for quantum technologies.
In this scenario, the assessment of the quantum work distribution has received
special attention and many experimental protocols have been proposed
in order to characterize this quantity in few particle in driven systems. In this
work, we study finite spin chains subject to driving potentials and calculate
the quantum work distribution in dynamical regimes that go from sudden quench
to adiabatic. We investigate the competition between interactions and dynamical
regimes and evaluate their impact in the behavior of the quantum work
distribution P (W ) as we increase the number of interacting particles and system size.
Our results show that the evolution of P (W ) is highly influenced by the
coupling regime which affects the number of accessible transitions of the system.
Based on our results, we discuss how the quantum work distribution can be used
as witness of phase transitions.