Non-local nature of deep thermalization

Quantum thermalization in a many-body system refers to the approach of local observables toward universal values, captured by a thermal Gibbs state. Recently, a novel generalized form of quantum thermalization was introduced, wherein a local subsystem is described by an ensemble of pure states, each of which is associated with a projective measurement outcome of the complementary subsystem. Remarkably, it was shown that the distribution of such states can under certain conditions approach a maximally entropic, uniform form, dubbed "deep thermalization". Here, we study the role of boundary conditions in governing the emergence of this dynamical phenomenon. Focusing on the maximally chaotic (1+1)-d kicked Ising model, we show that deep thermalization arises at late times for a small subsystem contained within the bulk of an infinitely large system, irrespective of the global topology. At finite times though, boundary effects do lead to observable differences: deep thermalization happens twice as fast for a system with periodic boundaries than with open boundaries. Our results reveal an inherent non-local feature associated with deep thermalization, in contrast to regular thermalization which is insensitive to boundary effects, owing to constraints placed on information propagation by Lieb-Robinson bounds.