An index for quantum cellular automata on fusion spin chains

February 13, 2024
1:50PM - 2:45PM
MW 154

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Add to Calendar 2024-02-13 13:50:00 2024-02-13 14:45:00 An index for quantum cellular automata on fusion spin chains Title:  An index for quantum cellular automata on fusion spin chainsSpeaker:  Junhwi Lim (Vanderbilt)Abstract:  The index for 1D quantum cellular automata (QCA) was introduced to measure the flow of the information by Gross, Nesme, Vogts, and Werner. Interpreting the index as the ratio of the Jones index for subfactors leads to a generalization of the index defined for QCA on more general abstract spin chains. These include fusion spin chains, which arise as the local operators invariant under a global (categorical/MPO) symmetry, and as the boundary operators on 2D topologically ordered spin systems. We introduce our generalization of index and show that it is a complete invariant for the group of QCA modulo finite depth circuits for the fusion spin chains built from the fusion category Fib. This talk is based on a joint work with Corey Jones.URL associated with Seminar:  https://www.asc.ohio-state.edu/math/vqss/ MW 154 Department of Mathematics math@osu.edu America/New_York public

Title:  An index for quantum cellular automata on fusion spin chains

Speaker:  Junhwi Lim (Vanderbilt)

Abstract:  The index for 1D quantum cellular automata (QCA) was introduced to measure the flow of the information by Gross, Nesme, Vogts, and Werner. Interpreting the index as the ratio of the Jones index for subfactors leads to a generalization of the index defined for QCA on more general abstract spin chains. These include fusion spin chains, which arise as the local operators invariant under a global (categorical/MPO) symmetry, and as the boundary operators on 2D topologically ordered spin systems. We introduce our generalization of index and show that it is a complete invariant for the group of QCA modulo finite depth circuits for the fusion spin chains built from the fusion category Fib. This talk is based on a joint work with Corey Jones.

URL associated with Seminar:  https://www.asc.ohio-state.edu/math/vqss/

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