Variational wave functions, ground state and their overlap

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 $E(\tau )$ 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.

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

References in corpus (4)

• Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
• Quantum phase transition in a two-dimensional system of dipoles
• Off-Diagonal Long-Range Order in Solid 4He
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• Quantum melting of a crystal of dipolar bosons
• Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids
• Two-dimensional Mixture of Dipolar Fermions: Equation of State and Magnetic Phases
• A Composite Fermion Approach to the Ultracold Dilute Fermi Gas
• Quantum Phase Transition with a Simple Variational Ansatz
• Feasibility of performing quantum chemistry calculations on quantum computers
• Hybrid between biologically and quantum-inspired many-body states