Translation invariant pure state on $\clb=\otimes_{\IZ}M_d(\IC)$ and its split property

Abstract

We prove that a real lattice symmetric reflection positive translation invariant pure state of $\clb=\otimes_{\IZ}M_d(\IC)$ is a split state if its two points spatial correlations functions decay exponentially.

arXiv admin note: text overlap with arXiv:0904.2104

References in corpus (2)

• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• Lieb-Robinson Bounds and the Exponential Clustering Theorem