TY - JOUR

T1 - On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature

AU - Konechny, Anatoly

AU - Friedan, Daniel

PY - 2004/7/16

Y1 - 2004/7/16

N2 - The boundary β 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 β 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.

AB - The boundary β 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 β 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.

U2 - 10.1103/PhysRevLett.93.030402

DO - 10.1103/PhysRevLett.93.030402

M3 - Article

SN - 0031-9007

VL - 93

JO - Physical Review Letters

JF - Physical Review Letters

IS - 3

M1 - 030402

ER -