![]() ![]() 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. 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. His research prior to 1978 was in particle physics, in particular the study of high-energy diffraction scattering. Research Fellow at All Souls College and a Professor of Theoretical Physics. The entanglement entropy and Schmidt number are the measures of entanglement in quantum many-body systems which are defined by the density matrix. Results are also presented for the time-dependence of S A starting from a general unentangled state. They also illustrate the connection between this zero-temperature entropy and the usual Gibbs-Boltzmann entropy. ![]() 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. One measure of the degree of quantum entanglement between Alice’s and Bob’s measurements is the von Neumann entropy S A=-Tr ρ Alog ρ A corresponding to A’s reduced density matrix ρ A. Alice can measure only observables localized within a subdomain A, and Bob can measure only those in the complement. Consider a quantum system with short-ranged interactions in some domain D, in its ground state. ![]()
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