Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-12-16
Phys.Rev.Lett. 93 (2004) 030402
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, Latex, 1 eps-figure; v2: some expository material added, a slightly more condensed version of the paper is publihed
Scientific paper
10.1103/PhysRevLett.93.030402
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.
Friedan Daniel
Konechny Anatoly
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