Error Bounds on the Universal Lindblad Equation in the Thermodynamic Limit

Abstract: It is a central problem in various fields of physics to elucidate the behavior of quantum many-body systems subjected to bulk dissipation. In this context, several microscopic derivations of the Lindblad quantum master equation for many-body systems have been proposed so far. Among them, the universal Lindblad equation derived by Nathan and Rudner is fascinating because it has desired locality and its derivation seems to rely solely on the assumption that the bath correlation time is much shorter than the dissipation time, which is the case in the weak-coupling limit or the singular-coupling limit. However, it remains elusive whether errors due to several approximations in deriving the universal Lindblad equation keep small during the time evolution in the thermodynamic limit. Here, rigorous error bounds on the time evolution of a local quantity are given, and it is shown that, under the assumption of the accelerated dissipation in bulk-dissipated systems, those errors vanish in the weak-coupling limit or the singular-coupling limit after taking the thermodynamic limit.