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Global climate change has become the greatest threat to mankind, endangering the ecological security of the earth and the long-term development of human society. Therefore, how to effectively reduce greenhouse gas emissions and curb the trend of global warming has become a common challenge facing all countries in the world. Fossil energy combustion is the fundamental cause of climate change. In this paper, the price return series of domestic energy and carbon markets are taken as the research objects. Firstly, the cross-correlation test is used to verify that there is an obvious cross-correlation between the return series of the energy and carbon markets. Based on this, the multifractal characteristics of energy market and carbon market cross-series are empirically studied. The empirical results show that there is an interactive correlation between energy and carbon markets and this relationship has multifractal characteristics; the interactive correlation between return series has multifractal characteristics. The long-range correlation between small fluctuations and large fluctuations and the fat tail distribution of return series are all reasons for the formation of multifractality. These conclusions will help to understand the non-linear dependence and potential dynamic mechanism between energy and carbon markets in China. [ABSTRACT FROM AUTHOR]