Prof John Cardy FRS

Abstract:

We consider the Rényi entropies Sn in one-dimensional massive integrable models diagonalizable by means of corner transfer matrices (such as Heisenberg and Ising spin chains). By means of explicit examples and using the relation of the corner transfer matrix with the Virasoro algebra, we show that close to a conformally invariant critical point, when the correlation length ξ is finite but large, the corrections to the scaling are of the unusual form ξ^-x/n, with x the dimension of a relevant operator in the conformal theory. This is reminiscent of the results for gapless chains and should be valid for any massive one-dimensional model close to a conformal critical point. © 2010 IOP Publishing Ltd and SISSA.

Abstract:

I discuss various aspects of the role of the conformal anomaly number c in two-and one + one-dimensional critical behaviour: its appearance as the analogue of Stefan's constant, its fundamental role in conformal field theory, in the classification of 2d universality classes, and as a measure of quantum entanglement, among other topics. © 2010 IOP Publishing Ltd and SISSA.