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Abstract:

Abstract If we partition a Hilbert space we can define the entanglement entropy (both von Neumann and Renyi) between the two pieces. We consider breaking up a system into two or more distinct spatial regions and ask about the entanglement between these two regions. 51�������ing the toric code ground state as an initial example, we show that there is an entanglement that scales as the length of the cut between the two regions, but there is also a sub-leading term, known as the topological entanglement entropy, which depends only on the topological properties of the system. While the leading term is nonuniversal, the topological term is robust and can be generalized to any other TQFT. We give three different derivations of the topological entanglement entropy.

Abstract:

Abstract An important process (discussed already in chapter 2) is the process by which a particle twists around its own axis. For a quantum mechanical particle this accumulates a phase associated with the particle’s spin. The particle spin is related in several ways to the R-matrix, and satisfies a number of important identities, including the ribbon identity.