Natural Sciences and Mathematics
A kink-based expression for the canonical partition function is developed using Feynman’s path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on the 3×3 Hubbard model and overcomes the sign problem seen in traditional path integral studies of fermion systems. Kinks correspond to transitions between different N-electron states, much in the same manner as occurs in configuration interaction calculations in standard ab initio methods. The different N-electron states are updated, based on which states occur frequently during a Monte Carlo simulation, giving better estimates of the true eigenstates of the Hamiltonian.
Hall, Randal W., "An Adaptive, Kink-based Approach to Path Integral Calculations" (2002). Collected Faculty and Staff Scholarship. 25.
Copyright © 2002 American Institute of Physics.
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