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Trace estimators allow 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 the exponential describing the Boltzmann weights. Here we report investigations of an alternative approach which employs Chebyshev polynomials. This method turns out to be also very accurate in general, but shows systematic inaccuracies at low temperatures that can be traced back to an improper behavior of the approximated density of states with and without smoothing kernel. Applications to archetypical quantum spin systems are discussed as examples., Comment: 11 pages, 16 figures

Carbon nanomembranes made from aromatic precursor molecules are free standing nanometer thin materials of macroscopic lateral dimensions. Although produced in various versions for about two decades not much is known about their internal structure. Here we present a first systematic theoretical attempt to model the formation, structure, and mechanical properties of carbon nanomembranes using classical molecular dynamics simulations. We find theoretical production scenarios under which stable membranes form. They possess pores as experimentally observed. Their Young's modulus, however, is systematically larger than experimentally determined., Comment: 12 pages, 18 figures

Classical carbon potentials together with classical molecular dynamics are employed to calculate structures and physical properties of such carbon-based materials where quantum mechanical methods fail either due to the excessive size, irregular structure or long-time dynamics. Examples are given by recently synthesized free-standing carbon nanomembranes (CNM) with molecular thickness and macroscopic lateral size as well as by amorphous carbon. Although such potentials, as for instance implemented in LAMMPS, yield reasonably accurate bond lengths and angles for several carbon materials such as graphene, it is not clear how accurate they are in terms of mechanical properties such as Young's moduli. We performed large-scale classical molecular dynamics investigations of three carbon-based materials using the various potentials implemented in LAMMPS as well as the highly sophisticated EDIP potential of Nigel Marks. We demonstrate how the Young's moduli vary with classical potentials and compare to experimental results. Since classical descriptions of carbon are bound to be approximations it is not astonishing that different realizations yield differing results. One should therefore carefully check for which observables a certain potential is suited. We hope to contribute to such a clarification., Comment: 12 pages, 5 figures