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Register a new userAdvanced Finite-Temperature Lanczos Method for anisotropic spin systems
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It is virtually impossible to evaluate the magnetic properties of large anisotropic magnetic molecules numerically exactly due to the huge Hilbert space dimensions as well as due to the absence of symmetries. Here we propose to advance the Finite-Temperature Lanczos Method (FTLM) to the case of single-ion anisotropy. The main obstacle, namely the loss of the spin rotational symmetry about the field axis, can be overcome by choosing symmetry related random vectors for the approximate evaluation of the partition function. We demonstrate that now thermodynamic functions for anisotropic magnetic molecules of unprecedented size can be evaluated.
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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. Instead we failed with the attempt. All investigated systems allow such approximations, only at temperatures of the order of the lowest energy gap the convergence is somewhat slower in the number of random vectors over which observables are averaged.
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