The Essence of Emergent Origins F: A Study on the Emergence Criteria and Characteristics of Exceptional Lie Group Topological Orders

zhou, changzheng, ZIQING zhou

Published Dec 5, 2025• 0 citations

Abstract

This paper, based on the three fundamental criteria of structural stability, information efficiency, and dynamical accessibility, systematically investigates the emergence characteristics of exceptional Lie group topological orders, including E, E, and E, for the first time. By analyzing the quantum dimension distribution, chiral central charge, and topological invariants of these exceptional Lie group systems, a universal theoretical description for exceptional Lie group topological orders is established. Numerical calculations show that within reasonable physical parameter ranges, systems such as E, E, E, and E all satisfy the emergence conditions for topological order, with structural stability criterion values SG > 3.0, information efficiency criterion values EG > 0.5, and dynamical accessibility criterion values DG > 0.99. In particular, the E topological order exhibits a unique ”vacuum uniqueness” property, with a total quantum dimension D = 1, offering a novel theoretical platform for topological quantum computation. This work advances topological order research to the frontier of mathematical physics, laying the foundation for exploring topological phases beyond the traditional Lie algebra framework

DOI: 10.5281/zenodo.17826018

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