Problematic smartphone use negatively affects physical and mental health. Despite the wide range of prior research, existing persuasive techniques are not flexible enough to provide dynamic persuasion content based on users' physical contexts and mental states. We first conducted a Wizard-of-Oz study (N=12) and an interview study (N=10) to summarize the mental states behind problematic smartphone use: boredom, stress, and inertia. This informs our design of four persuasion strategies: understanding, comforting, evoking, and scaffolding habits. We leveraged large language models (LLMs) to enable the automatic and dynamic generation of effective persuasion content. We developed MindShift, a novel LLM-powered problematic smartphone use intervention technique. MindShift takes users' in-the-moment app usage behaviors, physical contexts, mental states, goals \& habits as input, and generates personalized and dynamic persuasive content with appropriate persuasion strategies. We conducted a 5-week field experiment (N=25) to compare MindShift with its simplified version (remove mental states) and baseline techniques (fixed reminder). The results show that MindShift improves intervention acceptance rates by 4.7-22.5% and reduces smartphone usage duration by 7.4-9.8%. Moreover, users have a significant drop in smartphone addiction scale scores and a rise in self-efficacy scale scores. Our study sheds light on the potential of leveraging LLMs for context-aware persuasion in other behavior change domains.