Finite Temperature Dynamical Correlations using the Microcanonical Ensemble and the Lanczos Algorithm

Abstract

We show how to generalise the zero temperature Lanczos method for calculating dynamical correlation functions to finite temperatures. The key is the microcanonical ensemble, which allows us to replace the involved canonical ensemble with a single appropriately chosen state; in the thermodynamic limit it provides the same physics as the canonical ensemble but with the evaluation of a single expectation value. We can employ the same system sizes as for zero temperature, but whereas the statistical fluctuations present in small systems are prohibitive, the spectra of the largest system sizes are surprisingly smooth. We investigate, as a test case, the spin conductivity of the spin-1/2 anisotropic Heisenberg model and in particular we present a comparison of spectra obtained by the canonical and microcanonical ensemble methods.

11 pages, 9 figures

References in corpus (6)

• Transport and conservation laws
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Evidence for ideal insulating/conducting state in a 1D integrable system
• 17O NMR study of q=0 spin excitations in a nearly ideal S=1/2 1D Heisenberg antiferromagnet, Sr2CuO3, up to 800 K
• Low-temperature transport in Heisenberg chains
• Spin diffusion and the spin 1/2 XXZ chain at $T=\infty$ from exact diagonalization

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