Variational Approach for Many-Body Systems at Finite Temperature.

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Computational Physics

Background:

• Understanding the behavior of many-body systems is crucial in condensed matter physics.
• Existing methods often struggle with strong interaction regimes and complex quantum states.
• Accurate prediction of phase transitions requires robust theoretical frameworks.

Purpose of the Study:

• To introduce a novel equation for density matrices that guarantees monotonic free energy decrease.
• To develop a versatile variational approach applicable to a wide range of quantum many-body states.
• To investigate phase separation in the Holstein model under strong interaction conditions.

Main Methods:

• Formulation of a new equation for density matrices with guaranteed convergence to thermal equilibrium.
• Development of a generalized variational approach for bosonic and fermionic systems, including unitary transformations.
• Application of the method to the Holstein model on square lattices of varying sizes (20x20 and 50x50).

Main Results:

• The proposed equation ensures a monotonic decrease of free energy, reaching the Gibbs thermal state.
• The variational approach successfully handles complex quantum states, including generalized Gaussian states.
• Phase separation between superconducting and charge-density wave phases is predicted in the strong interaction regime of the Holstein model.

Conclusions:

• The new density matrix equation provides a stable and convergent method for studying thermal states.
• The generalized variational approach offers a powerful tool for investigating diverse many-body systems.
• The predicted phase separation highlights the complex interplay of phases in strongly interacting electron-phonon systems.