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We study the properties of a two-body random matrix ensemble fordistinguishable spins. We require the ensemble to be invariant under the groupof local transformations and analyze a parametrization in terms of the groupparameters and the remaining parameters associated with the "entangling" partof the interaction. We then specialize to a spin chain with nearest neighbourinteractions and numerically find a new type of quantum phase transitionrelated to the strength of a random external field i.e. the time reversalbreaking one body interaction term.

The two-body random spin ensemble and a new type of quantum phase transition