On the sharpness of the zero-entropy-density conjecture

Details On the sharpness of the zero-entropy-density conjecture On the sharpness of the zero-entropy-density conjecture

2005-07-07

arxiv.org/abs/math-ph/0507022v3

J. Math. Phys. 46, 123301 (2005)

Physics

Mathematical Physics

11 pages, references added, corrected typos

Scientific paper

10.1063/1.2138047

The zero-entropy-density conjecture states that the entropy density, defined as the limit of S(N)/N at infinity, vanishes for all translation-invariant pure states on the spin chain. Or equivalently, S(N), the von Neumann entropy of such a state restricted to N consecutive spins, is sublinear. In this paper it is proved that this conjecture cannot be sharpened, i.e., translation-invariant states give rise to arbitrary fast sublinear entropy growth. The proof is constructive, and is based on a class of states derived from quasifree states on a CAR algebra. The question whether the entropy growth of pure quasifree states can be arbitrary fast sublinear was first raised by Fannes et al. [J. Math. Phys. 44, 6005 (2003)]. In addition to the main theorem it is also shown that the entropy asymptotics of all pure shift-invariant nontrivial quasifree states is at least logarithmic.

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