  We present a wave function representation for the canonical ensemble thermal
density matrix by projecting the thermofield double state against the desired
number of particles. The resulting canonical thermal state obeys an imaginary
time-evolution equation. Starting with the mean-field approximation, where the
canonical thermal state becomes an antisymmetrized geminal power wave function,
we explore two different schemes to add correlation: by number-projecting a
correlated grand-canonical thermal state, and by adding correlation to the
number-projected mean-field state. As benchmark examples, we use
number-projected configuration interaction and an AGP-based perturbation theory
to study the Hydrogen molecule in a minimal basis and the six-site Hubbard
model.
