Stability of the low-temperature multi-Q phase

Determine whether the multi-Q phase in the parameter regime 2.1t ≤ μ ≤ 2.2t is stable by including higher-order terms in the Landau free energy, and establish whether those terms induce a first-order transition.

Background

For the triangular-lattice extended Hubbard model with SU(N) exchange interaction, the quartic Ginzburg–Landau coefficients indicate a multi-Q state in part of the parameter regime above the Van Hove singularity, specifically near 2.1t ≤ μ ≤ 2.2t. However, the quartic analysis alone may not determine the stability of this phase, so higher-order terms in the Landau expansion are required to resolve whether the multi-Q state persists or is replaced by another phase through a first-order transition.

References

Note that the multi-$Q$ phase in the low-temperature regime around $2.1t\leq \mu \leq 2.2 t$ may not be stable and higher orders need to be taken into account in the Landau free energy (see App.~\ref{app:singlemulti}), potentially inducing a first-order transition.

— Unconventional bond- and current-density waves on hexagonal lattices  (2608.19185 - Szabo et al., 19 Aug 2026) in Section 4, “Microscopic model”; Appendix B, Section “Single- vs. multi-Q order”