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). 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. It remains open whether the boundary entropy is always bounded below.
Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854-8019, USA. friedan@physics.rutgers.edu
Daniel
D
Friedan
Anatoly
A
Konechny