  We investigate crossing behavior of ground state entanglement Renyi entropies
of quantum critical systems. We find a novel property that the ground state in
one quantum phase cannot be locally transferred to that of another phase, that
means a global transformation is necessary. This also provides a clear evidence
to confirm the long standing expectation that entanglement Renyi entropy
contains more information than entanglement von Neumann entropy. The method of
studying crossing behavior of entanglement Renyi entropies can distinguish
different quantum phases well. We also study the excited states which still
give interesting results.

Quantum Physics