Prof John Cardy FRS

Abstract:

We review the conformal field theory approach to entanglement entropy in 1+1 dimensions. We show how to apply these methods to the calculation of the entanglement entropy of a single interval, and the generalization to different situations such as finite size, systems with boundaries and the case of several disjoint intervals. We discuss the behaviour away from the critical point and the spectrum of the reduced density matrix. Quantum quenches, as paradigms of non-equilibrium situations, are also considered. © 2009 IOP Publishing Ltd.

Abstract:

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr ρAⁿ for any integer n is calculated as the four-point function of twist fields of a particular type and the final result is expressed in a compact form in terms of the Riemann-Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data. © 2009 IOP Publishing Ltd.

Abstract:

We consider a quantum quench in a system of free bosons, starting from a thermal initial state. As in the case where the system is initially in the ground state, any finite subsystem eventually reaches a stationary thermal state with a momentum-dependent effective temperature. We find that this can, in some cases, even be lower than the initial temperature. We also study lattice effects and discuss more general types of quenches. Copyright © 2009 EPLA.Association.