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Path Integral Studies Of The 2d Hubbard Model Using A New Projection Operator, Randall W. Hall
Path Integral Studies Of The 2d Hubbard Model Using A New Projection Operator, Randall W. Hall
Collected Faculty and Staff Scholarship
Feynman’s path integral formulation of quantum mechanics, supplemented by an approximate projection operator (exact in the case of noninteracting particles), is used to study the 2D Hubbard model. The projection operator is designed to study Hamiltonians defined on a finite basis set, but extensions to continuous basis sets are suggested. The projection operator is shown to reduce the variance by a significant amount relative to straightforward Monte Carlo integration. Approximate calculations are usually within one standard deviation of exact results and virtually always within two to three standard deviations. In addition, the algorithm scales with the number of discretization points …
Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall
Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall
Collected Faculty and Staff Scholarship
Feynman’s path integral formulation of quantum mechanics is used to study the correlated electronic states of Na4–Na6. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born–Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our results …