@article{4a32df3c989f42f99308a5318bd67121,
title = "Boundary entropy of one-dimensional quantum systems at low temperature",
abstract = "A gradient formula for the boundary β function, was proved. The formula eliminates the possibility of esoteric asymptotic behavior under renormalization. The gradient formula was expressed as the gradient of the boundary entropy s at fixed nonzero temperature. The basic principles of quantum mechanics and locality were used, and the formula implied equally that the boundary entropy decreased with temperature.",
author = "Daniel Friedan and Anatoly Konechny",
note = "Funding Information: We would like to thank G. Moore and A. B. Zamolodchikov for stimulating discussions. We especially thank G. Moore for pointing out a deficiency in an early version of the proof. This work was supported by the Rutgers New High Energy Theory Center, which A. K. thanks for warm hospitality. The work of A. K. was supported in part by BSF-American-Israel Bi-National Science Foundation, the Israel Academy of Sciences and Humanities-Centers of Excellence Program, and the German-Israel Bi-National Science Foundation.",
year = "2004",
month = jul,
day = "16",
doi = "10.1103/PhysRevLett.93.030402",
language = "English (US)",
volume = "93",
pages = "030402--1--030402--4",
journal = "Physical review letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "3",
}