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Many-Body Chern Number without Integration
Koji Kudo1, Haruki Watanabe2, Toshikaze Kariyado3
1Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan.
Physical Review Letters
|May 4, 2019
Summary
The many-body Chern number, crucial for understanding quantized Hall conductance, can be computed more efficiently. Numerical calculations show integration over boundary conditions is unnecessary, reducing computational cost.
Area of Science:
- Condensed Matter Physics
- Topological Matter
Background:
- The Niu, Thouless, and Wu work established the many-body Chern number for quantized Hall conductance with interactions.
- The generalized Chern number formulation involves integration over twisted boundary conditions, posing physical and computational challenges.
Purpose of the Study:
- To investigate the necessity of integration in the generalized many-body Chern number formulation.
- To identify a more computationally efficient method for calculating topological invariants in interacting systems.
Main Methods:
- Numerical calculations were employed to analyze the integrand of the generalized Chern number.
- The behavior of the integrand was studied with respect to system size and twisted boundary conditions.
Main Results:
- The integrand of the many-body Chern number was found to be effectively quantized on its own.
- The error associated with omitting the integration decays exponentially with increasing system size.
Conclusions:
- Integration over all twisted boundary conditions for the many-body Chern number is unnecessary.
- Significant reduction in numerical cost for computing the many-body Chern number is achievable by evaluating the Berry connection at a single twisted boundary condition for large systems.
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