Work distribution for strongly coupled many-body open quantum systems

Abstract

The non-equilibrium quantum thermodynamics of many-body open systems is notoriously rich, especially in the strong-coupling regime where strong system-bath correlations develop and interactions produce non-perturbative effects. Such systems can be described by `quantum impurity models'where the system and bath are treated on an equal footing as a single composite. Paradigmatic examples are the spin-boson and Anderson impurity models, in which system degrees of freedom interact with either bosonic or fermionic gapless baths. Here we study the quantum work distribution function (WDF) of such systems following a quench. Capturing the full continuum of many-body excitations in the WDF requires a non-perturbative solution of the underlying non-equilibrium quantum impurity problem. For this purpose, we extend the time-dependent numerical renormalization group (TDNRG) approach to the calculation of the WDF, which applies directly in the thermodynamic limit, can be used for arbitrary quench amplitudes at zero or finite temperature, and provides exponentially fine low-energy resolution. Our numerically-exact solution reveals power-law threshold behavior due to the Anderson orthogonality catastrophe when the work approaches its minimum value, with universal scaling collapse of the distribution below an emergent low-energy scale induced by system-bath correlations.