One-plaquette Chern number: Many-body Chern number without integration

The Niu-Thouless-Wu formula defines the many-body version of the Chern number that characterizes the quantized Hall conductance in the presence of disorders or interactions. In this talk, we provide numerical evidence that the integration by twisted angles in the Niu-Thouless-Wu formula is unnecessary if the system size and the excitation gap are sufficiently large. The Berry curvature itself is effectively quantized and the error decays exponentially with the system size. The lack of integration reduces the computational cost, which is advantageous in the interacting many-body problems for a sufficiently large system size. We also discuss the accuracy of the effective quantization in the vicinity of quantum phase transitions.