2 00 9 Translation invariant pure state and its split property
نویسنده
چکیده
In this paper we refined a criteria investigated in [BJKW] for a translation invariant factor state on one dimensional lattice to be pure. However the central aim here is to prove that such a condition is also necessary for a translation invariant factor state to be pure. As an easy fall out we also prove that a translation invariant pure state admits Haag duality property. Further a real lattice symmetric translation invariant pure state admits split property if the spacial correlation functions decay exponentially. The last result supports a conjecture originally proposed by Taku Matsui [Ma2] for translation invariant pure states.
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