Abstract
This paper is a contribution to the theory of coherent crystals. We present arguments claiming that negative minima in the Fourier transform of a soft pair interaction may give rise to the coexistence of diagonal and off-diagonal long-range orders at high densities, and that this coexistence may be detectable due to a periodicity seen on the off-diagonal part of the one-body reduced density matrix, without breaking translation invariance. As an illustration, we study the ground state of a homogenous system of bosons in continuous space, from the interaction retaining only the Fourier modes v(k) belonging to a single nonzero wave number |k|=q. The result is a mean-field model. We prove that for v(k)>0 the ground state is asymptotically fully Bose condensed, while for v(k)<0 at densities exceeding a multiple of ℏ2q2/2m|v(k)| it exhibits both Bose–Einstein condensation and diagonal long-range order, and the latter can be seen on both the one- and the two-body density matrix.
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