The metal-insulator transition driven by strong electronic correlations – generically called the "Mott" transition – is usually described entirely by electronic Hamiltonians, with models designed to exhibit related emergent phenomena such as magnetism and superconductivity.
In real solids, the electronic localization also couples to the crystal lattice, and it turns out that these elastic degrees of freedom insert important new entropic phenomena. The coupling to the lattice induces elastic strain fields, which have intrinsic long-range interactions that cannot be screened. When strain fields are produced as a secondary order parameter in phase transitions - as for example in ferroelectrics - this produces unexpected consequences for the dynamics of order parameter fluctuations. A very important class of transition metal oxides – the perovskites – can be thought of as an array of tethered octahedra where the Mott transition produces a shape-change in the unit cell. Coupling of the fundamental order parameter to octahedral rotations gives rise to large entropic effects that can shift the transition temperature by hundreds of degrees K. This insight might offer ways to make better cooling systems by enhancing caloric effects.
[1] Elastic interactions and control of the Mott transition, G. G. Guzmán-Verri, R. T. Brierley, P. B. Littlewood, arXiv:1701.02318.
[2] Landau theory and giant room-temperature barocaloric effect in MF3 metal trifluorides, A. Corrales-Salazar, R. T. Brierley, P. B. Littlewood, G. Guzmán-Verri, Phys. Rev. Mat. (2017).
[3] Why is the electrocaloric effect so small in ferroelectrics?, G. G. Guzmán-Verri, P. B. Littlewood, APL Mater. 4, 064106 (2016).