MONITORING OF THE CHANGE IN COASTAL ENVIRONMENT IN SOUTHERN PART OF RED-RIVER DELTA FROM SATELLITE IMAGES AND THE MECHANISM OF BEACH EROSION

Joint Research on Environmental Science and Technology for the Eart

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

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

Surgical Treatment for Skeletal Metastases From Soft Tissue Sarcomas: Experience With 23 Lesions in 20 Patients

Purpose. This paper reports the procedures and the clinical results of a series of surgical treatments for skeletal metastases from soft tissue sarcomas