Resolve whether the candidate CDW phase is gapped

Determine whether the candidate charge-density-wave phase of the extended checkerboard-lattice Fermi-Hubbard model at ν=1/3 is gapped or gapless in the thermodynamic limit by means of reliable large-scale calculations such as density-matrix renormalization group studies.

Background

Exact-diagonalization calculations show robust Bragg peaks in the candidate charge-density-wave regime, supporting translational-symmetry breaking. However, finite-size scaling of the charge gap gives only a small extrapolated value, and the accessible clusters are insufficient to decide whether the phase is insulating or metallic in the thermodynamic limit.

The authors consequently retain the qualification “candidate CDW” and explicitly identify the gapped-versus-gapless character as unresolved.

References

Therefore, determining whether the phase is gapped or gapless requires more numerical evidence from reliable large-scale calculations such as DMRG, which is beyond the scope of this work. Although the metallic/insulating conclusion cannot drawn on current ED-accessible geometries, we refer to this regime as ``candidate CDW'', as the Bragg peak for connected static structure factor is sharp and robust.

— HyperDet Wavefunction: A Phase-Agnostic Ansatz for Strongly Correlated Systems  (2609.04146 - Hu et al., 3 Sep 2026) in Appendix, Section “Exact-Diagonalization Diagnostics for the Fermionic Phase Diagram,” subsection “Diagnostics of the Candidate CDW Phase”