Entanglement Entropy in Extended Systems
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 SA=-Tr ρAlog ρA corresponding to A’s reduced density matrix ρA. 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 SA starting from a general unentangled state. This work was carried out with P. Calabrese.
Speaker Details
Research Fellow at All Souls College and a Professor of Theoretical Physics. His research prior to 1978 was in particle physics, in particular the study of high-energy diffraction scattering. After this, he applied methods of quantum field theory and the renormalization group to condensed matter, especially to critical phenomena in both pure and disordered equilibrium and non-equilibrium systems. In the 1980s he helped develop the theory of conformal invariance and its applications to these problems, ideas which also had an impact in string theory and quantum gravity.Cardy is a Fellow of the Royal Society, a recipient of the 2000 Paul Dirac Medal and Prize of the Institute of Physics, and of the 2004 Lars Onsager Prize of the American Physical Society.
- Date:
- Speakers:
- John Cardy
- Affiliation:
- University of Oxford
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Jeff Running
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