Accuracy of the typicality approach using Chebyshev polynomials

• URL: http://arxiv.org/abs/2104.13218v2
• Date: Mon, 31 May 2021 07:56:38 GMT
• Title: Accuracy of the typicality approach using Chebyshev polynomials
• Authors: H. Schl\"uter, F. Gayk (Bielefeld University), H.-J. Schmidt (Osnabr\"uck University), A. Honecker (CY Cergy Paris Universit\'e), J. Schnack (Bielefeld University)
• Abstract summary: Trace estimators allow to approximate thermodynamic equilibrium observables with astonishing accuracy. Here we report an approach which employs Chebyshev an alternative approach describing the exponential expansion of space weights. This method turns out to be also very accurate in general, but shows systematic inaccuracies at low temperatures.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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