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arXiv:cond-mat/0211165 · Physical review. B, Condensed matter

Low-temperature Lanczos method for strongly correlated systems

Markus Aichhorn, Maria Daghofer, Hans Gerd Evertz, Wolfgang von der Linden

Published Apr 24, 2003• 81 citations
arXivHTMLPDF

Abstract

We present a modified finite-temperature Lanczos method for the evaluation of dynamical and static quantities of strongly correlated electron systems that complements the finite-temperature method introduced by Jakli\ifmmode \check{c}\else \v{c}\fi{} and Prelov\ifmmode \check{s}\else \v{s}\fi{}ek for low temperatures. Together they allow accurate calculations at any temperature with moderate effort. As an example we calculate the static spin-correlation function and the regular part of the optical conductivity ${\ensuremath{\sigma}}^{\mathrm{reg}}(\ensuremath{\omega})$ of the one-dimensional Hubbard model at half filling and show in detail the connection between the ground-state and finite-temperature method. By using cluster perturbation theory, the finite-temperature spectral function is extended to the infinite system, clearly exhibiting the effects of spin-charge separation.

DOI
10.1103/physrevb.67.161103

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We present a modified finite-temperature Lanczos method for the evaluation of dynamical and static quantities of strongly correlated electron systems that complements the finite-temperature method introduced by Jakli\ifmmode \check{c}\else \v{c}\fi{} and Prelov\ifmmode \check{s}\else \v{s}\fi{}ek for low temperatures. Together they allow accurate calculations at any temperature with moderate effort. As an example we calculate the static spin-correlation function and the regular part of the optical conductivity \ensuremathσreg(\ensuremathω){\ensuremath{\sigma}}^{\mathrm{reg}}(\ensuremath{\omega})\ensuremathσreg(\ensuremathω) of the one-dimensional Hubbard model at half filling and show in detail the connection between the ground-state and finite-temperature method. By using cluster perturbation theory, the finite-temperature spectral function is extended to the infinite system, clearly exhibiting the effects of spin-charge separation.
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The Exact Diagonalization method is a powerful numerical tool to study Quantum Many Body systems on finite clusters. In particular, using this technique one can accurately calculate energy and momentum dependent dynamic correlation functions which are observable in scattering experiments, such as Neutron Scattering, Raman Scattering, and Photoemission Spectroscopy which measures the spectral function of the system. Here we give an outline of the Lanczos method with special emphasis on the evaluation of dynamical quantities.
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