Diabolical textures from spatially embedded Thouless pumps yield distinct gapped states separated by trap-scaling critical points that terminate into unnecessary critical surfaces when the texture varies rapidly, with a classification framework based on Kitaev's Ω spectrum conjecture.
Trap-size scaling in confined particle systems at quantum transitions
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abstract
We develop a trap-size scaling theory for trapped particle systems at quantum transitions. As a theoretical laboratory, we consider a quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We discuss trap-size scaling at the Mott insulator to superfluid transition in the Bose-Hubbard model. We present exact and accurate numerical results for the XY chain and for the low-density Mott transition in the hard-core limit of the one-dimensional Bose-Hubbard model. Our results are relevant for systems of cold atomic gases in optical lattices.
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2026 1verdicts
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Topological Phenomena Protected by Diabolical Textures
Diabolical textures from spatially embedded Thouless pumps yield distinct gapped states separated by trap-scaling critical points that terminate into unnecessary critical surfaces when the texture varies rapidly, with a classification framework based on Kitaev's Ω spectrum conjecture.