Lower bound on the entropy of boundaries and junctions in 1+1d quantum critical systems

TL;DR

This is the first general restriction on the possible values of g for bulk critical systems with c≥1 on the bulk conformal central charge and Δ1>(c-1)/12 on the most relevant bulk scaling dimension.

Abstract

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

Figures (1)

• Figure 1: The $N=1$ bound for $c=1$ compared to the minimum value of $g^{2}$ for the $c=1$ gaussian model. The comparison is extended past the maximal value $\Delta_1=1/2$ by interpreting $\Delta_1$ as the lowest dimension of a primary occurring in the boundary state.