Exact Diagonalization of SU(N) Fermi-Hubbard Models.

Area of Science:

• Condensed matter physics
• Quantum many-body systems
• Strongly correlated electron systems

Background:

• Exact diagonalization is crucial for understanding quantum many-body models.
• SU(N) Fermi-Hubbard models are relevant for studying systems with multiple internal "colors" or flavors.
• Previous methods faced challenges in scaling with system size and particle number.

Purpose of the Study:

• To develop an efficient method for exact diagonalization of SU(N) Fermi-Hubbard models.
• To utilize representation theory for simplifying Hamiltonian matrix elements.
• To investigate the stability of SU(N) phases under varying interaction strengths.

Main Methods:

• Employed representation theory of the unitary group U(L).
• Constructed an orthonormal basis using semistandard Young tableaux or Gelfand-Tsetlin patterns.
• Performed exact diagonalizations on L-site clusters for various SU(N) symmetries.

Main Results:

• Demonstrated a simplified Hamiltonian in the chosen basis.
• Investigated the robustness of SU(N) phases by decreasing on-site interaction U.
• Observed the emergence of a long-range color ordered phase for N=4 at 1/4 filling on a triangular lattice.

Conclusions:

• The developed method provides a powerful tool for studying SU(N) Fermi-Hubbard models.
• Representation theory offers a systematic way to handle complex many-body systems.
• The findings highlight the rich phase diagram of SU(N) models, with potential for new emergent phenomena.