Local Variational Principle

Details Local Variational Principle Local Variational Principle

2002-09-06

arxiv.org/abs/cond-mat/0209151v2

Phys. Rev. E 66, 066133 (2002)

Physics

Condensed Matter

Statistical Mechanics

15 pages, 5 figures, one more section added

Scientific paper

10.1103/PhysRevE.66.066133

A generalization of the Gibbs-Bogoliubov-Feynman inequality for spinless particles is proven and then illustrated for the simple model of a symmetric double-well quartic potential. The method gives a pointwise lower bound for the finite-temperature density matrix and it can be systematically improved by the Trotter composition rule. It is also shown to produce groundstate energies better than the ones given by the Rayleigh-Ritz principle as applied to the groundstate eigenfunctions of the reference potentials. Based on this observation, it is argued that the Local Variational Principle performs better than the equivalent methods based on the centroid path idea and on the Gibbs-Bogoliubov-Feynman variational principle, especially in the range of low temperatures.

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