Partition function zeros of quantum many-body systems

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics

Background:

• Yang-Lee zeros are crucial for understanding phase transitions in statistical mechanics.
• Calculating these zeros for complex models like the Hubbard model is computationally challenging.

Purpose of the Study:

• To present a novel method for calculating Yang-Lee partition function zeros.
• To apply this method to translationally invariant lattice fermion models, specifically the Hubbard model.

Main Methods:

• The method utilizes a theorem relating Yang-Lee zeros to single-electron self-energy in the Matsubara formulation.
• Yang-Lee zeros are mapped to spin- and wave-vector-labeled virtual energies.
• These virtual energies are solutions to a specific set of equations involving the self-energy and chemical potential.

Main Results:

• A new theoretical framework for computing Yang-Lee zeros has been established.
• The method provides a way to determine virtual energies that correspond to the partition function zeros.
• Demonstrated applicability through examples in simplified scenarios.

Conclusions:

• The presented method offers an effective approach to calculating Yang-Lee zeros for lattice fermion systems.
• This work provides a valuable tool for studying critical phenomena and phase transitions in condensed matter physics.
• The mapping to virtual energies simplifies the analysis of complex many-body systems.