2003/12/31 by Daniel Friedan, Anatoly Konechny · 4 citations
Physics and Astronomy · #hep-th #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.93.030402
published as Phys.Rev.Lett. 93 (2004) 030402 · 12 pages, Latex, 1 eps-figure; v2: some expository material added, a slightly more condensed version of the paper is publihed in Phys. Rev. Lett
arxiv created 2004/08/06 · arxiv updated 2009/12/01
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 non-zero temperature. The gradient formula implies that s decreases under renormalization except at critical points (where it stays constant). At a critical point, the number exp(s) is the ``ground-state degeneracy,'' g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature except at critical points, where it is independent of temperature. The boundary thermodynamic energy u then also decreases with temperature. It remains open whether the boundary entropy of a 1-d quantum system is always bounded below. If s is bounded below, then u is also bounded below.