Variational Neural and Tensor Network Approximations of Thermal States

Understand

We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy.

• This approach directly approximates the state at a fixed temperature, allowing for systematic improvement of the ansatz expressiveness without accumulating errors from iterative imaginary time evolution.
• We employ a variety of trial states -- both tensor networks as well as neural networks -- as variational Ans\"atze for our numerical optimization.
• We benchmark and compare different constructions in the above classes, both for one- and two-dimensional problems, with systems made of up to $N=100$ spins.