Lower bound on the entropy of boundaries and junctions in (1+1)-dimensional quantum critical systems.

A lower bound is derived for the boundary entropy s=lng of a (1+1)-dimensional quantum critical system with boundary under the conditions c≥1 on the bulk conformal central charge and Δ1>(c-1)/12 on the most relevant bulk scaling dimension. This is the first general restriction on the possible values of g for bulk critical systems with c≥1.

Boundary entropy of one-dimensional quantum systems at low temperature.

The boundary beta function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s decreases under renormalization, except at critical points (where it stays constant).