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Title:
Operator-algebraic approach to topological phases
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Abstract:
The thermodynamic limit of topologically ordered systems can be studied using an operator-algebraic description. Not only does this yield a clean mathematical framework amenable to a rigorous analysis, it also opens up the possibility of using deep results in operator algebra not available for finite systems. In this talk I will give an example of this by looking at the total quantum dimension, an invariant of topological phases related to the anyonic excitations a topologically ordered state supports. In particular, I show howb one can use Jones' index of subfactors to find the total quantum dimension. This leads to an interpretation of the logarithm of the total quantum dimension as an entropic quantity, related to a quantum information task. In the end this gives an alternative to the topological entanglement entropy. Based on joint work with Leander Fiedler and Tobias Osborne.
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