Entanglement Entropy in Extended Systems

Опубликовано 6 сентября 2016, 5:37

Consider a quantum system with short-ranged interactions in some domain D, in its ground state. Alice can measure only observables localized within a subdomain A, and Bob can measure only those in the complement. One measure of the degree of quantum entanglement between Alice's and Bob's measurements is the von Neumann entropy $S_A=-Tr \rho_A\log\rho_A$ corresponding to A's reduced density matrix $\rho_A$. In this talk I review path integral methods for computing this and discuss how the form of the results depends on (a) the geometry and (b) whether the system is at a quantum critical point. They also illustrate the connection between this zero-temperature entropy and the usual Gibbs-Boltzmann entropy.  Results are also presented for the time-dependence of $S_A$ starting from a general unentangled state. This work was carried out with P. Calabrese.