  Variational methods are a common approach for computing properties of ground
states but have not yet found analogous success in finite temperature
calculations. In this work we develop a new variational finite temperature
algorithm (VAFT) which combines ideas from minimally entangled typical thermal
states (METTS), variational Monte Carlo (VMC) optimization and path integral
Monte Carlo (PIMC). This allows us to define an implicit variational density
matrix to estimate finite temperature properties in two and three dimensions.
We benchmark the algorithm on the bipartite Heisenberg model and compare to
exact results.
