Rigorous Results on the Ground State of the Attractive SU(N) Hubbard Model

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Mechanics

Background:

• The SU(N) Hubbard model is crucial for understanding strongly correlated electron systems.
• Particle-hole symmetry is a key feature in many quantum models, simplifying analysis.
• Bipartite lattices are fundamental structures in condensed matter, appearing in various materials.

Purpose of the Study:

• To rigorously determine the ground-state properties of the attractive SU(N) Hubbard model.
• To establish theoretical theorems for identifying degeneracy, fermion number, and SU(N) quantum numbers.
• To investigate the conditions under which charge density wave order emerges.

Main Methods:

• Development and application of three novel mathematical theorems.
• Analysis of the attractive SU(N) Hubbard model on bipartite lattices.
• Consideration of systems with varying sublattice sizes (|N_{A}-N_{B}|).

Main Results:

• Three theorems are proven, enabling precise identification of ground-state properties.
• The SU(N) quantum number and fermion number of the ground state are determined.
• Charge density wave order is shown to occur when sublattice sizes differ significantly.

Conclusions:

• The established theorems provide a robust framework for analyzing SU(N) Hubbard models.
• The findings are applicable to bipartite lattices in any dimension, irrespective of translation invariance.
• The study offers new insights into symmetry and ordering in quantum many-body systems.