On the boundary entropy of one-dimensional quantum systems at low temperature
Dec, 200312 pages
Published in:
- Phys.Rev.Lett. 93 (2004) 030402
e-Print:
- hep-th/0312197 [hep-th]
Report number:
- RU-NHETC-2003-39
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Citations per year
Abstract:
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.- 64.60.Ak
- 11.25.Uv
- 05.30.-d
- entropy
- quantum theory
- renormalisation
- critical points
- statistical mechanics
- critical phenomena
- universality
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