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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 $(0,1)$.
In this paper we extend the results of Lenci and Rey-Bellet on the large deviation upper bound of the distribution measures of local Hamiltonians with respect to a Gibbs state, in the setting of translation-invariant finite-range interactions. We sho
Linearity of a dynamical entropy means that the dynamical entropy of the n-fold composition of a dynamical map with itself is equal to n times the dynamical entropy of the map for every positive integer n. We show that the quantum dynamical entropy i
We consider the Heisenberg XXZ spin-$J$ chain ($Jinmathbb{N}/2$) with anisotropy parameter $Delta$. Assuming that $Delta>2J$, and introducing threshold energies $E_{K}:=Kleft(1-frac{2J}{Delta}right)$, we show that the bipartite entanglement entropy (
We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution
This paper continues the work Y. Suhov, M. Kelbert. FK-DLR states of a quantum bose-gas, arXiv:1304.0782 [math-ph], and focuses on infinite-volume bosonic states for a quantum system (a quantum gas) in a plane. We work under similar assumptions upon