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

Abstract

We study trace estimators for equilibrium thermodynamic observables that rely on the idea of typicality and derivatives thereof such as the finite-temperature Lanczos method (FTLM). As numerical examples quantum spin systems are studied. Our initial aim was to identify pathological examples or circumstances, such as strong frustration or unusual densities of states, where these methods could fail. It turned out that all investigated systems allow such approximations. Only at temperatures of the order of the lowest energy gap is the convergence somewhat slower in the number of random vectors over which observables are averaged.