2023/03/28 by Jingbo Wang, Wang, Jingbo
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum and electron transport phenomena
paper · pdf · doi:10.48550/arxiv.2303.15760
openalex publication_date 2023/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Topological order (long-range entanglement) is a new type of order that beyond Landau's symmetry breaking theory. This concept plays important roles in modern condensed matter physics. The topological entanglement entropy provides a universal quantum number to characterize the topological order in a system. The topological entanglement entropy of the BTZ black hole was calculated and found that it coincides with that for fractional quantum Hall states. So the BTZ black hole has the same topological order with the fractional quantum Hall state. We show that the four dimensional black hole can also have topological order, by showing that the topological entanglement entropy of black holes is non-zero in loop quantum gravity. We also consider the Hamiltonian constraint in loop quantum gravity. By comparing with the BF theory, we found that the physical Hilbert space for loop quantum gravity is degenerate on non-trivial manifold, which indicate the existence of topological order in loop quantum gravity. We advise to bring in the methods and results in string-net condensation to loop quantum gravity to solve some difficult problems.