Nonergodic classical correlations lead to ergodic quantum correlations in low-dimensional spin models

Quantum correlations are traditionally viewed as constituted out of classical correlations and single-party parameters. While this, of course, remains so, we show that entanglement can have statistical mechanical properties like ergodicity, which are not inherited from the corresponding classical correlations and single-party parameters, in diagonalizable as well as nondiagonalizable low-dimensional quantum spin systems. In particular, we find that the results hold for the quantum XY spin models on the chain, ladder and in two dimensions