Entanglement Renormalization of Thermofield Double States

Entanglement renormalization is a method for coarse-graining quantum state in real space, with the multi-scale entanglement ansatz (MERA) as notable example. We obtain an scheme finite-temperature (Gibbs) states by applying MERA to their canonical purification, thermofield double state. As example, we find analytically exact circuit finite temperature two-dimensional toric code which maps it coarse-grained system renormalized higher temperature, thus explicitly demonstrating its lack of topological order. Furthermore, apply this one-dimensional free boson models at and that corresponding critical thermal described Lifshitz theory. numerically demonstrate relevance irrelevance various perturbations under space renormalization.