A Tight Lower Bound to the Ground-State Energy

Area of Science:

• Quantum mechanics
• Computational chemistry

Background:

• Temple's lower bound for ground-state energy, derived 90 years ago, is often inaccurate compared to Rayleigh Ritz upper bounds.
• The inaccuracy stems from its reliance on the Hamiltonian's second moment.

Purpose of the Study:

• To enhance Temple's lower bound for ground-state energy estimation.
• To improve the accuracy of the overlap squared between true and approximate ground-state wave functions.

Main Methods:

• Improving Temple's lower bound for overlap squared.
• Generalizing and detailing a recent improvement using higher-order basis functions from the Arnoldi algorithm.

Main Results:

• Combined improvements yield a more accurate lower bound for ground-state energy.
• Demonstrated accuracy comparable to upper bounds using a quartic potential example.

Conclusions:

• The enhanced method provides a more reliable lower bound for ground-state energies.
• Applicable to diverse quantum systems, including atoms and molecules.