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What is Undecidability of Spectral Gap in Quantum Systems about?

The paper demonstrates that the spectral gap problem for 2D translationally-invariant, nearest-neighbour quantum spin systems is undecidable, meaning no algorithm can determine if such a system is gapped or gapless. This undecidability holds even under strong conditions regarding the uniqueness of the ground state and the relationship between the spectral gap and interaction strength. The findings imply that the spectral gap problem is axiomatic independent, indicating that certain Hamiltonians exist for wh

Author

Francisco Galvez

Language

EN