Survival of Hartree–Fock density-wave phases beyond mean field

Determine whether the coherent density-wave, excitonic-supersolid, and coherent Wigner-crystal phases predicted by unrestricted Hartree–Fock theory in the $\nu_T=1$ lowest-Landau-level bilayer survive as distinct thermodynamic phases after correlations beyond Hartree–Fock are included.

Background

Within Hartree–Fock and time-dependent Hartree–Fock, the roton instability near d/ℓ≃1.175d/\ell\simeq1.175 produces a coherent pseudospin-density wave rather than directly destroying interlayer coherence. At larger separation, unrestricted Hartree–Fock also finds coherent crystalline states.

The paper stresses that these results concern an uncontrolled approximation. Correlation effects may preempt or eliminate the density-wave phases, but the authors do not establish their fate.

References

Whether these phases exist beyond HF is not known; our expectation is that they do not (Sec.~\ref{qh:sec:beyond}).

— Exciton superfluidity in two-dimensional bilayers at zero and high magnetic fields  (2610.22037 - Sarma et al., 15 Oct 2026) in Section 10.5, “Beyond Hartree-Fock at $\nu_T=1$: expectations”; Section 10.7, “Broken translation symmetry and supersolids”