Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians

We propose characterization of the three-dimensional topological insulator by using the Chern number for the entanglement Hamiltonian (entanglement Chern number). Here we take the extensive spin partition of the system, that pulls out the quantum entanglement between up spin and down spin of the many-body ground state. In three dimensions, the topological insulator phase is described by the section entanglement Chern number, which is the entanglement Chern number for a periodic plane in the Brillouin zone. The section entanglement Chern number serves as an interpolation of the Z2 invariants defined on time-reversal invariant planes. We find that the change of the section entanglement Chern number protects the Weyl point of the entanglement Hamiltonian, and the parity of the number of Weyl points distinguishes the strong topological insulator phase from the weak topological insulator phase

Phase diagram of a disordered higher-order topological insulator: A machine learning study

A higher-order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a considerable interest. Yet, its robustness against disorders is still unclear. In this work, we investigate a phase diagram of higher-order topological insulator phases in a breathing kagome model in the presence of disorders by using a state-of-the-art machine learning technique. We find that the corner states survive against the finite strength of disorder potential as long as the energy gap is not closed, indicating the stability of the higher-order topological phases against the disorders

Entanglement Chern Number of the Kane–Mele Model with Ferromagnetism

The entanglement Chern number, the Chern number for the entanglement Hamiltonian, is used to characterize the Kane–Mele model, which is a typical model of the quantum spin Hall phase with time-reversal symmetry. We first obtain the global phase diagram of the Kane–Mele model in terms of the entanglement spin Chern number, which is defined by using a spin subspace as a subspace to be traced out in preparing the entanglement Hamiltonian. We further demonstrate the effectiveness of the entanglement Chern number without time-reversal symmetry by extending the Kane–Mele model to include the Zeeman term. The numerical results confirm that the sum of the entanglement spin Chern number is equal to the Chern number