Exploring non-linear correlators on AGP

Area of Science:

• Quantum Chemistry
• Computational Physics
• Strong Correlation Problem

Background:

• Standard methods like coupled cluster theory excel for weakly correlated systems.
• Strongly correlated systems require more sophisticated quantum mechanical approaches.
• Antisymmetrized geminal power (AGP) shows promise as a reference for strong correlation.

Purpose of the Study:

• To investigate non-linear exponential Ansätze as improvements over linear correlators for AGP.
• To explore two novel computational methods for tackling strong correlation.
• To benchmark these new approaches against the pairing Hamiltonian.

Main Methods:

• Similarity transformed Hamiltonian with a Hilbert-space Jastrow operator, projected Schrödinger equation over AGP.
• Approximation of the unitary pair-hopper Ansatz for quantum computing applications.
• Benchmark numerical calculations for the ground state of the pairing Hamiltonian.

Main Results:

• Demonstrated the summability of the similarity transformed Hamiltonian to all orders.
• Successfully applied and benchmarked two distinct non-linear Ansätze.
• Provided numerical evidence for the efficacy of the proposed methods on the pairing Hamiltonian.

Conclusions:

• Non-linear exponential Ansätze offer a promising avenue for treating strongly correlated systems.
• The investigated methods provide accurate solutions for the pairing Hamiltonian.
• These advancements contribute to more robust computational tools in quantum chemistry.