Definitions of entanglement entropy of spin systems in the valence-bond basis

The valence-bond structure of spin-1/2 Heisenberg antiferromagnets is closely related to quantum entanglement. We investigate measures of entanglement entropy based on transition graphs, which characterize state overlaps in the overcomplete valence-bond basis. The transition graphs can be generated using projector Monte Carlo simulations of ground states of specific hamiltonians or using importance-sampling of valence-bond configurations of amplitude-product states. We consider definitions of entanglement entropy based on the bonds or loops shared by two subsystems (bipartite entanglement). Results for the bond-based definition agrees with a previously studied definition using valence-bond wave functions (instead of the transition graphs, which involve two states). For the one dimensional Heisenberg chain, with uniform or random coupling constants, the prefactor of the logarithmic divergence with the size of the smaller subsystem agrees with exact results. For the ground state of the two-dimensional Heisenberg model (and also Neel-ordered amplitude-product states), there is a similar multiplicative violation of the area law. In contrast, the loop-based entropy obeys the area law in two dimensions, while still violating it in one dimension - both behaviors in accord with expectations for proper measures of entanglement entropy.Comment: 9 pages, 8 figures. v2: significantly expande

Construction 3D BIM-based knowledge management system: a case study

Knowledge management (KM) is the organization, creation, sharing and flow of knowledge within organizations. Knowledge can be shared and reused among involved engineers and experts to improve a construction process and reduce the time and cost of solving problems. This paper proposes a new and practical methodology to capture and represent construction project knowledge by using a Building Information Modeling (BIM) approach. Using BIM approach, users can make visual knowledge management in the 3D Computer-aided Design (CAD) environment. This study addresses the application of knowledge management in the construction phase of construction projects and proposes a Construction BIM-based Knowledge Management (CBIMKM) system for general contractors. The CBIMKM is then applied in selected case studies of a construction building project in Taiwan to verify our proposed methodology and demonstrate the effectiveness of sharing knowledge in the 3D environment. By applying the BIM approach, all participants in a project can share and reuse explicit and tacit knowledge through the 3D CAD-based knowledge map. The combined results demonstrate that the CBIMKM system can be used as a visual 3D-based knowledge management platform by utilizing the BIM approach and web technology