Develop a unified many-electron theory of Peierls transitions

Develop a many-electron theory for real transition-metal materials that simultaneously describes the dimerized low-temperature phase and the disordered high-temperature phase while incorporating all relevant local and nonlocal interactions.

Background

The review emphasizes that real transition-metal compounds combine band formation, molecular-orbital bonding, electron–electron correlations, orbital degrees of freedom, lattice distortions, and fluctuating high-temperature structures. Existing treatments often address only selected ingredients or idealized limits, whereas experiments show that local clusters can persist above the long-range structural transition.

A comprehensive theory would therefore need to treat the dimerized and thermally disordered phases on the same footing and describe both local chemical bonding and nonlocal cooperative effects. The authors identify the absence of such a theory as a major unresolved theoretical problem.

References

Therefore, even the seemingly simple situation of V${4+}$ ($d1$) dimers in VO$_2$ still attracts a lot of attention. While considerable progress had already been achieved in the early stages of Peierls transition studies by taking into account electron-phonon interaction of different forms, disorder, and fluctuations, a true many-electron theory for real materials that describes both the dimerized and the high-temperature disordered phase, including all relevant local and non-local interactions, has yet to be developed.

— Orbital-Induced Peierls Transitions: How Orbitals Orchestrate Lattice Instability  (2609.18614 - Mizokawa et al., 16 Sep 2026) in Section "Peierls OR NOT REALLY Peierls: LOCAL EFFECTS"

One of the most interesting question is how sensitive these transitions to the $d$-band filling.

— Orbital-Induced Peierls Transitions: How Orbitals Orchestrate Lattice Instability  (2609.18614 - Mizokawa et al., 16 Sep 2026) in Section "QUASI ONE-DIMENSIONAL LATTICES"

Another important question is which approximation should be used to study possible nesting and instability in chi0. Typically, one considers nonmagnetic DFT calculations, but interactions can do more than just renormalize the electronic spectrum close to the Fermi level.

— Orbital-Induced Peierls Transitions: How Orbitals Orchestrate Lattice Instability  (2609.18614 - Mizokawa et al., 16 Sep 2026) in Section "CALCULATION AND EXPERIMENTAL METHODS—Theoretical methods"

And even more delicate question is whether strong Coulomb correlations should be taken into consideration in a static way, as is done in the DFT+U approximation, or whether methods such as dynamical mean-field theory (DMFT) with a frequency-dependent self-energy (which properly renormalizes the electronic structure close to $E_F$) must be used.

— Orbital-Induced Peierls Transitions: How Orbitals Orchestrate Lattice Instability  (2609.18614 - Mizokawa et al., 16 Sep 2026) in Section "CALCULATION AND EXPERIMENTAL METHODS—Theoretical methods"