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• W3099335426 abstract "We specialize a recently-proposed determinant formula for the overlap of the zero-momentum N'eel state with Bethe states of the spin-1/2 XXZ chain to the case of an odd number of downturned spins, showing that it is still of Gaudin-like form, similar to the case of an even number of down spins. We generalize this result to the overlap of $q$-raised N'eel states with parity-invariant Bethe states lying in a nonzero magnetization sector. The generalized determinant expression can then be used to derive the corresponding determinants and their prefactors in the scaling limit to the Lieb-Liniger (LL) Bose gas. The odd number of down spins directly translates to an odd number of bosons. We furthermore give a proof that the N'eel state has no overlap with non-parity-invariant Bethe states. This is based on a determinant expression for overlaps with general Bethe states that was obtained in the context of the XXZ chain with open boundary conditions. The statement that overlaps with non-parity-invariant Bethe states vanish is still valid in the scaling limit to LL which means that the BEC state has zero overlap with non-parity-invariant LL Bethe states." @default.
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• W3099335426 date "2014-08-01" @default.
• W3099335426 modified "2023-10-15" @default.
• W3099335426 title "Néel-XXZ state overlaps: odd particle numbers and Lieb–Liniger scaling limit" @default.
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• W3099335426 doi "https://doi.org/10.1088/1751-8113/47/34/345003" @default.
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