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Fragmented and symmetry-restored condensates in a three-site Bose ring: exchange versus umklapp
We study $N$ bosons on a three-site ring with nearest-neighbour hopping, density-assisted hopping of the opposite sign, and an on-site interaction, written equivalently as three momentum modes $q=0,\pm1$ with a channel-dependent quartic vertex. As the density-assisted term grows it inverts the band,
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