With their recent development, large language models (LLMs) have been found to exhibit a certain level of Theory of Mind (ToM), a complex cognitive capacity that is related to our conscious mind and that allows us to infer another's beliefs and perspective. While human ToM capabilities are believed to derive from the neural activity of a broadly interconnected brain network, including that of dorsal medial prefrontal cortex (dmPFC) neurons, the precise processes underlying LLM's capacity for ToM or their similarities with that of humans remains largely unknown. In this study, we drew inspiration from the dmPFC neurons subserving human ToM and employed a similar methodology to examine whether LLMs exhibit comparable characteristics. Surprisingly, our analysis revealed a striking resemblance between the two, as hidden embeddings (artificial neurons) within LLMs started to exhibit significant responsiveness to either true- or false-belief trials, suggesting their ability to represent another's perspective. These artificial embedding responses were closely correlated with the LLMs' performance during the ToM tasks, a property that was dependent on the size of the models. Further, the other's beliefs could be accurately decoded using the entire embeddings, indicating the presence of the embeddings' ToM capability at the population level. Together, our findings revealed an emergent property of LLMs' embeddings that modified their activities in response to ToM features, offering initial evidence of a parallel between the artificial model and neurons in the human brain.