We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.
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| http://dx.doi.org/10.1103/PhysRevLett.100.087205 | DOI Listing |
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