Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates

The authors investigate approximations of the partition function that can be used for large systems where an exact evaluation is impossible. These methods rest on the observation that traces can be replaced by expectation values with respect to a single random vector for not too small temperatures. At low temperatures, where single vectors produce strongly fluctuating approximations, a proper average over many random vectors yields quasi exact results.