We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of $n$ sites in a system of length $L$ generically grows as $\ensuremath{\sigma}\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}[2\ensuremath{\pi}en(L\ensuremath{-}n)∕L]+C$, where $\ensuremath{\sigma}$ is the on-site spin and $C$ is a function depending only on magnetization.We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of $n$ sites in a system of length $L$ generically grows as $\ensuremath{\sigma}\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}[2\ensuremath{\pi}en(L\ensuremath{-}n)∕L]+C$, where $\ensuremath{\sigma}$ is the on-site spin and $C$ is a function depending only on magnetization.

arXiv:quant-ph/0506209Physical Review ASep 22, 200538 citations

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n

sites in a system of length

L

generically grows as $\ensuremath{\sigma}\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}[2\ensuremath{\pi}en(L\ensuremath{-}n)∕L]+C$, where $\ensuremath{\sigma}$ is the on-site spin and

C

is a function depending only on magnetization.