A demonstration of the finite-temperature upside-down adiabatic connection with the asymmetric Hubbard dimer

The finite-temperature upside-down adiabatic connection is an integral expression for the exchange-correlation free energy, a quantity of interest in simulations of planetary cores and fusion experiments. This approach smoothly connects a thermal ensemble of strictly correlated electrons to one with realistic interaction strength, while requiring that the density of the system remain fixed across all interaction strengths. The asymmetric Hubbard dimer allows for an exact demonstration of finite-temperature adiabatic connections. The properties of the upside-down adiabatic connection in a variety of regimes will be presented using this exactly solvable model, along with discussion of their usefulness within the generalized thermal adiabatic connection approach.