Thermal stitching: Extending the reach of quantum fermion solvers

For quantum fermion problems, many accurate solvers are limited by the temperature regime in which they can be usefully applied. The Mermin theorem implies the uniqueness of an effective potential from which both the exact density and free energy at a target temperature can be found, via a calculation at a different, reference temperature. We derive exact expressions for both the potential and the free energy in such a calculation, and introduce three controllable approximations that reduce the cost of such calculations. We illustrate the effective potential and its free energy, and test the approximations, on the asymmetric two-site Hubbard model at finite temperature.