Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems

Area of Science:

• Quantum mechanics
• Computational chemistry
• Condensed matter physics

Background:

• Accurate representation of thermal states is crucial for understanding quantum systems.
• Existing methods often struggle with particle number conservation in thermal ensembles.

Purpose of the Study:

• To develop a novel wave function representation for the canonical ensemble thermal density matrix.
• To incorporate particle number projection into thermal state calculations.
• To benchmark the proposed method against established techniques.

Main Methods:

• Projecting the thermofield double state onto a desired particle number.
• Developing two schemes to add electron correlation to the mean-field state.
• Utilizing number-projected configuration interaction and AGP-based perturbation theory.

Main Results:

• The proposed method generates canonical thermal states obeying an imaginary-time evolution.
• The antisymmetrized geminal power (AGP) serves as a mean-field approximation.
• Successful application to the hydrogen molecule and the six-site Hubbard model.

Conclusions:

• The developed wave function representation provides an accurate and efficient way to study canonical thermal states.
• The correlation schemes effectively improve upon the mean-field approximation.
• This work offers a valuable tool for quantum many-body simulations.