Variational wave functions, ground state and their overlap

Details Variational wave functions, ground state and their overlap Variational wave functions, ground state and their overlap

2007-02-28

arxiv.org/abs/cond-mat/0703004v2

Phys. Rev. Lett. 99, 030403 (2007)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures, to be published in Phys. Rev. Lett. (revised version)

Scientific paper

10.1103/PhysRevLett.99.030403

An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The overlap is simply related to the area under the $E(\tau)$ curve, i.e. the energy as a function of imaginary time. This has important applications to, for example, quantum Monte-Carlo algorithms where the overlap becomes as a simple byproduct of routine simulations. As a result, we find that the practical definition of a good variational wave function for quantum Monte-Carlo simulations, {\it i.e.} fast convergence to the ground state, is equivalent to a good overlap with the actual ground state of the system.

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