Thermal stitching: Extending the reach of quantum fermion solvers

TL;DR

This paper introduces a method called thermal stitching that extends quantum fermion solvers to a broader temperature range by deriving exact expressions for effective potentials and free energies, and testing approximations on a Hubbard model.

Contribution

The authors derive exact formulas for effective potentials and free energies at different temperatures and propose three approximations to make calculations more efficient.

Findings

Derived exact expressions for potential and free energy.

Tested approximations on the Hubbard model.

Demonstrated extended temperature applicability of quantum fermion solvers.

Abstract

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.