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Variational wave functions, ground state and their overlap

Christophe Mora·Xavier Waintal
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Abstract

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 $E(τ)$ 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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BibTeXRIS

Christophe Mora, Xavier Waintal. 2007-06-26. Variational wave functions, ground state and their overlap. https://doi.org/10.1103/physrevlett.99.030403

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