Universal scaling theory for the ordered-phase two-point correlations

Develop theoretical predictions for the universal scaling behavior of two-point correlations in the ordered phase of finite-size ultracold lattice Bose gases, corresponding to negative rescaled distance \(\zeta<0\), where off-diagonal long-range order may produce substantial corrections to scaling.

Background

The paper demonstrates a strong collapse of the rescaled momentum-density data in the disordered phase, where the observed universal scaling function is consistent with the Fourier transform of a Yukawa correlation form. The corresponding collapse is less satisfactory in the ordered phase, which is associated with ζ<0\zeta<0.

The authors identify two unresolved theoretical issues in this regime: there is no theoretical prediction available for the relevant scaling behavior, and off-diagonal long-range order may generate stronger finite-size corrections. Consequently, establishing the ordered-phase universal scaling function remains an open problem directly connected to extending the paper’s two-scale-factor-universality analysis.

References

In the ordered phase we find that the data collapse is not as good as in the disordered case. We leave the study of this regime for the future as we are not aware of a theoretical prediction for \zeta <0, where the presence of off-diagonal long-range order might introduce more pronounced corrections to scaling for our finite system size.

— Universal scaling of fluctuations and correlations across the superfluid transition  (2609.03433 - Paquiez et al., 3 Sep 2026) in Section “Universal scaling functions of two-point correlations”