  Minimally entangled typical thermal states (METTS) are a construction that
allows one to to solve for the imaginary time evolution of quantum many body
systems. By using wave functions that are weakly entangled, one can take
advantage of efficient representations in the form of matrix product states. We
generalize these ideas to arbitrary variational wave functions and we focus, as
illustration, on the particular case of restricted Boltzmann machines. The
imaginary time evolution is carried out using stochastic reconfiguration
(natural gradient descent), combined with Monte Carlo sampling. Since the time
evolution takes place on the tangent space, deviations between the actual path
in the Hilbert space and the trajectory on the variational manifold can be
important, depending on the internal structure and expressivity of the
variational states. We show how these differences translate into a rescaled
temperature and demonstrate the application of the method to quantum spin
systems in one and two spatial dimensions.
