Finding the Right Density from the Wrong Temperature with Thermal Density Functional Theory

Using the Mermin theorem, we define a correction to the one-body potential that ensures that a calculation performed at some reference temperature generates the exact density at some other desired temperature. We list various properties of this potential and derive a simple approximation for the free energy at the desired temperature. We calculate this effective thermal potential exactly for the two-site Hubbard model, and find that our free-energy approximation is highly accurate under many conditions.