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Informal PhD Exit Seminar: On the stability of charges in infinite quantum spin systems

Mathematical Physics & Probability

Speaker: Matthew Cha, UC Davis
Related Webpage: https://www.math.ucdavis.edu/~mmcha/
Location: 2112 MSB
Start time: Wed, Jun 7 2017, 4:10PM

We consider a family of charge superselection sectors in infinite quantum spin systems corresponding to almost localized endomorphisms. If the vacuum state is pure and satisfies certain locality conditions, we show how to recover the charge statistics. In particular, the superselection structure is that of a braided tensor category. Further, we introduce a superselection criterion selecting excitations with energy below a threshold. When the threshold energy falls in a gap of the spectrum of the vacuum state, we prove that stability of the spectral gap implies stability of the superselection structure. We apply our results to prove stability of anyons in Kitaev's quantum double.

This is joint work with Pieter Naaijkens and Bruno Nachtergaele.