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Split states of the quasi-local algebra

Student-Run Applied & Math Seminar

Speaker: Alvin Moon, UC Davis
Related Webpage: https://www.math.ucdavis.edu/~asmoon/
Location: 2112 MSB
Start time: Thu, Feb 21 2019, 12:30PM

States of C* algebras are the generalization of probability measures. In this talk, we discuss an interpretation of statistical independence of states with respect to the left and right infinite subsystems of the spin chain quasi-local algebra, known as the split property. We review formulations of the split property in the context of spin chains as well as its recent applications to the study of gapped classification of symmetry protected topological (SPT) phases, by Y. Ogata, and Lieb-Schultz-Mattis type theorems, by Y. Ogata and H. Tasaki. We also sketch a proof that the split property is a stable feature of an SPT phase.