Time Averaged Density Matrix as an Optimization Problem

A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor networks, as, e.g., matrix product operators (MPO). An algorithm is explained and several results for non-integrable Ising chains are given. Among them are scaling examples, time averaged expectation values, their variances and operator space entanglement entropies.