English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We specialize a recently-proposed determinant formula for the overlap of thezero-momentum N\'eel state with Bethe states of the spin-1/2 XXZ chain to thecase 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. Wegeneralize this result to the overlap of $q$-raised N\'eel states withparity-invariant Bethe states lying in a nonzero magnetization sector. Thegeneralized determinant expression can then be used to derive the correspondingdeterminants 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 ofbosons. We furthermore give a proof that the N\'eel state has no overlap withnon-parity-invariant Bethe states. This is based on a determinant expressionfor overlaps with general Bethe states that was obtained in the context of theXXZ chain with open boundary conditions. The statement that overlaps withnon-parity-invariant Bethe states vanish is still valid in the scaling limit toLL which means that the BEC state has zero overlap with non-parity-invariant LLBethe states.

N\'eel-XXZ state overlaps: odd particle numbers and Lieb-Liniger scaling limit