Recurrent Neural Network approximations of thermal states through Rényi ensembles

Recurrent neural networks have been shown to be effective variational ansatze for the representation of ground state wavefunctions of strongly correlated Hamiltonians. Their autoregressive nature allows for the efficient generation of samples and their expressivity allows for excellent variational exploration of the optimization landscape. In this work, we use recurrent neural networks (RNNs) to approximate density matrices at thermal equilibrium, focusing our initial efforts on various strongly correlated spin Hamiltonians. Instead of the Gibbs ensemble, we use the thermodynamic ensembles that minimize the Rényi free energy introduced in Phys. Rev. B 103, 205128 (2021). We find that our optimized density matrices perform very well compared to the analytically derived density matrices that minimize the Renyi free energy for several quantum spin systems.