Accuracy of the typicality approach using Chebyshev polynomials

Abstract Trace estimators allow us to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finite-temperature Lanczos method (FTLM) which relies on a Krylov space expansion of exponential describing Boltzmann weights. Here we report investigations an alternative approach employs Chebyshev polynomials. This turns out be also very accurate in general, but shows systematic inaccuracies at low temperatures that can traced back improper behavior approximated density states and without smoothing kernel. Applications archetypical quantum spin systems are discussed as examples.