Quantum entanglement is a fundamental and important tool to probe the properties of a variety of physical systems such as black holes in astrophysics, quantum phase transition in condensed matter physics, and photosynthesis in biophysics. Their scaling is found to be consistent with conformal field theory (CFT) predictions and recent results of particle number fluctuation calculations. In this work, we simultaneously explore the geometric and edge contributions in the integer quantum Hall (IQH) state and its edge reconstruction in a unified bipartite method. Furthermore, if a non-smooth sharp angle is in the presence of the subsystem boundary, a universal angle dependent geometric contribution is expected to appear in the subleading correction. It is referred to as topological EE which is related to the quantum dimension of the collective excitation in the bulk. Moreover, the subleading correction exists in long-range entangled topological phases. However, the so-called area law is violated logarithmically in a quantum critical phase. Generally speaking, entanglement entropy (EE) between two subregions of a gapped quantum many-body state is proportional to the area/length of their interface due to the short-range quantum correlation. ![]()
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