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. 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.

11 pages, 14 figures, minor improvements, thicker lines in figures, new error estimate (13)

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Cited by in corpus (5)

• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Flat-band physics in the spin-1/2 sawtooth chain
• Melting of magnetization plateaus for kagome and square-kagome lattice antiferromagnets
• Spin-half Heisenberg antiferromagnet on a symmetric sawtooth chain: Rotation-invariant Green's functions and high-temperature series
• A spectrum adaptive kernel polynomial method