Isometric tensor network representations of two-dimensional thermal states

Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite temperature simulations in two dimensions is a continuing challenge. Here, we use the class of recently introduced isometric tensor network states (isoTNS), which can also be directly realized with unitary gates on a quantum computer. We utilize a purification ansatz to efficiently represent thermal states of the transverse field Ising model. By performing an imaginary time evolution starting from infinite temperature, we find that this approach offers a new way with low computational complexity to represent states at finite temperatures.