Compare the free energies of coexisting metallic and insulating solutions

Derive and compare the free energies of the coexisting metallic and insulating dynamical mean-field theory solutions for expanded SrVO3 in order to characterize their relative stability and identify the thermodynamically selected phase.

Background

The expanded SrVO3 calculations exhibit coexistence between metallic and insulating DMFT solutions over a finite region. The phase diagram is inferred from solution tracking and hysteresis, but a thermodynamic free-energy comparison would be required to establish which branch is globally stable and to locate the equilibrium transition more rigorously. The authors state that their impurity solver does not currently provide the required free-energy expression.

References

In order to further characterize the stability of this behavior, a free energy comparison of the two coexisting solution, similar to Ref., would be in order. At this moment, we do not have access to this expression within our employed impurity solver.

— Tuning crystal-fields by He-irradiation and orbital Widom line in SrVO$_3$ films  (2608.14362 - Pickem et al., 14 Aug 2026) in Section 5, subsection “Phase diagram and validation to experiment,” footnote in the discussion of the coherent insulating solution