Entropy growth of shift-invariant states on a quantum spin chain
Fannes, M. ; Haegeman, B. ; Mosonyi, M.
arXiv, 0306055 / Harvested from arXiv
Text on arXiv
We study the entropy of pure shift-invariant states on a quantum spin chain. Unlike the classical case, the local restrictions to intervals of length $N$ are typically mixed and have therefore a non-zero entropy $S_N$ which is, moreover, monotonically increasing in $N$. We are interested in the asymptotics of the total entropy. We investigate in detail a class of states derived from quasi-free states on a CAR algebra. These are characterised by a measurable subset of the unit interval. As the entropy density is known to vanishes, $S_N$ is sublinear in $N$. For states corresponding to unions of finitely many intervals, $S_N$ is shown to grow slower than $(\log N)^2$. Numerical calculations suggest a $\log N$ behaviour. For the case with infinitely many intervals, we present a class of states for which the entropy $S_N$ increases as $N^\alpha$ where $\alpha$ can take any value in $(0,1)$.
Publié le : 2003-06-23
Classification:  Mathematical Physics,  Quantum Physics 
@article{0306055,
     author = {Fannes, M. and Haegeman, B. and Mosonyi, M.},
     title = {Entropy growth of shift-invariant states on a quantum spin chain},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0306055}
}

Fannes, M.; Haegeman, B.; Mosonyi, M. Entropy growth of shift-invariant states on a quantum spin chain. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0306055/