Exact mean-field overestimation factor for the critical temperature

Determine the exact factor by which the fermionic matrix-product-state-plus-mean-field framework overestimates the superconducting critical temperature, particularly for the two-dimensional bilayer mixed-dimensional systems studied in the paper.

Background

The matrix-product-state-plus-mean-field framework is argued to reproduce the dependence of the critical temperature on microscopic parameters while systematically overestimating its absolute value because of the mean-field component. Previous work suggests that the overestimate is approximately a quasi-constant factor, potentially of order four in the relevant setting, but the precise factor has not been established. This uncertainty limits quantitative interpretation of the predicted critical temperatures.

References

The one unknown at present is the exact factor by which, e.g., $T_c$ is overestimated.

— Predicting critical temperature in quantum simulators for high-$T_c$ superconductivity: the matrix product state plus mean field approach  (2608.18861 - Köhler et al., 19 Aug 2026) in Section 3.2, subsection “Critical temperature”