On the sharpness of the zero-entropy-density conjecture -: art. no. 123301

The zero-entropy-density conjecture states that the entropy density defined as s:=lim(N ->infinity)S(N)/N 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 [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. (c) 2005 American Institute of Physics.