Undecidability of the spectral gap - PubMed

pubmed.ncbi.nlm.nih.gov
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The spectral gap--the energy difference between the ground state and first excited state of a system--is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang-Mills ga …
The spectral gap--the energy difference between the ground state and first excited state of a system--is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang-Mills gap conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it…
Cubitt Ts Perez-Garcia D Wolf Mm, Bausch J, Cubitt Ts, Watson Jd., Et Al., Lemm M, Sandvik Aw, Wang L., Laumann Cr, Moessner R
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