Translation Invariant Pure State on \otimes _{{\mathbb {Z}}}\!M_d({\mathbb {C}}) and Haag Duality |
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Authors: | Anilesh Mohari |
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Institution: | 1. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600113, India
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Abstract: | We prove Haag duality property of any translation invariant pure state on ${\mathcal B}= \otimes _{{\mathbb {Z}}}\!M_d({\mathbb {C}}), d \ge 2$ , where $M_d({\mathbb {C}})$ is the set of $d \times d$ dimensional matrices over the field of complex numbers. We also prove a necessary and sufficient condition for a translation invariant factor state to be pure on ${\mathcal B}$ . |
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