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The bulk spectral gap is certifiable from above but uncomputable from below

Xu, Xiangling et al.
arXiv (All) · Papers
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mathematical-physicsquantum-physicsstatistical-mechanics
Determining spectral gaps in the thermodynamic limit is a central challenge in quantum many-body physics. When a fixed boundary condition is imposed, this problem is undecidable: no algorithm, even with unlimited resources, can decide for every Hamiltonian whether it is gapped. Yet the thermodynamic
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