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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
PubMed
Summary
This summary is machine-generated.

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.

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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.