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arXiv · 1402.3585

Stabilizing Canonical-Ensemble Calculations in the Auxiliary-Field Monte Carlo Method

C. N. Gilbreth·Y. Alhassid
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Abstract

Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the auxiliary-field Monte Carlo (AFMC) method, low-temperature or large-model-space calculations require numerically stabilized matrix multiplication. When adapting methods used in the grand-canonical ensemble to the canonical ensemble of fixed particle number, the numerical stabilization increases the number of required floating-point operations for computing observables by a factor of the size of the single-particle model space, and thus can greatly limit the systems that can be studied. We describe an improved method for stabilizing canonical-ensemble calculations in AFMC that exhibits better scaling, and present numerical tests that demonstrate the accuracy and improved performance of the method.

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C. N. Gilbreth, Y. Alhassid. 2014-02-14. Stabilizing Canonical-Ensemble Calculations in the Auxiliary-Field Monte Carlo Method. https://doi.org/10.1016/j.cpc.2014.09.002

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