Variational wave functions and their overlap with the ground state.
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 simulations where the overlap becomes as a simple by-product of routine simulations. As a result, we find that the practical definition of a good variational wave function for quantum Monte Carlo simulations, i.e., fast convergence to the ground state, is equivalent to a good overlap with the actual ground state of the system.
Laboratoire Pierre Aigrain, Département de Physique, Ecole Normale Supérieure, 24 rue Lhomond, F-75005 Paris, France.
Christophe
C
Mora
Xavier
X
Waintal