Understanding under which conditions physical systems thermalize is a long-standing question in many-body physics. While generic quantum systems thermalize, there are known instances where thermalization is hindered, for example in many-body localized (MBL) systems. Here we introduce a class of stochastic collision models coupling a many-body system out of thermal equilibrium to an external heat bath. We derive upper and lower bounds on the size of the bath required to thermalize the system via such models, under certain assumptions on the Hamiltonian. We use these bounds, expressed in terms of the max-relative entropy, to characterize the robustness of MBL systems against externally-induced thermalization. Our bounds are derived within the framework of resource theories using the convex split lemma, a recent tool developed in quantum information. We apply our results to the disordered Heisenberg chain, and numerically study the robustness of its MBL phase in terms of the required bath size.

理解物理系统在何种条件下会热化是多体物理学中一个长期存在的问题。尽管通用量子系统发生热化，但在某些情况下，例如在多体局部（MBL）系统中，热化受到阻碍。在这里，我们介绍了一类随机碰撞模型，该模型将不平衡的多体系统耦合到外部热浴。在哈密顿量的某些假设下，我们通过此类模型得出了使系统热化所需的浴池大小的上限和下限。我们使用以最大相对熵表示的这些界限来表征MBL系统针对外部诱导的热化的鲁棒性。我们的界限是在资源理论的框架内使用凸分裂引理（一种在量子信息中开发的最新工具）得出的。