Interacting Chern Insulator in Infinite Spatial Dimensions

Area of Science:

• Condensed matter physics
• Topological insulators
• Many-body physics

Background:

• Chern insulators exhibit unique topological properties.
• Hubbard interactions introduce electronic correlations.
• High-dimensional limits simplify complex many-body problems.

Purpose of the Study:

• Investigate a Chern insulator model with Hubbard interactions in arbitrary even dimension D.
• Analyze the model's behavior in the D→∞ limit.
• Characterize the topological phases and their transitions.

Main Methods:

• Dynamical mean-field theory (DMFT) applied to the D→∞ limit.
• Analysis of the phase diagram, including correlated Mott and trivial band insulators.
• Investigation of the distinction between insulating and semimetal states.

Main Results:

• The model is well-defined and nontrivial in the D→∞ limit.
• DMFT predicts a phase diagram with a continuum of topologically distinct phases.
• Topological phases are characterized by a nonquantized Chern density in the D→∞ limit.

Conclusions:

• The interplay of topology and correlation is crucial in high dimensions.
• The D→∞ limit provides a tractable framework for studying complex topological phases.
• Non-quantized topological invariants emerge in the thermodynamic limit.