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As a new kind of topological order combining topology and geometry, fracton orders have attracted attentions from various domains for its theoretical novelty and potential implication for quantum information. The mobility of particles in fracton orders is restricted in lower dimensional subsystems of certain geometry, which is deeply rooted in novel entanglement patterns. In this talk, I will introduce a series of fracton ordered exactly solvable models which include not only point-like particles but also spatially extended excitations such that both mobility and deformability are restricted. We construct Hamiltonians, ground state wavefunctions and excitations, and study several exotic properties such as ground state degeneracies. We establish a program of entanglement renormalization for these fixed-point wavefunctions, rendering a hierarchy of entanglement patterns. Finally, I will demonstrate our exploration on subsystem symmetry protected topological orders, which are dual to fracton orders, focusing on the idea of strange correlators and generation of subsystem symmetries via higher-order cellular automata. The talk will be ended with several future directions.

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Meng-Yuan Li, SYSU
Seminar Room 0.03, ETP
Contact: Guo-Yi Zhu / Simon Trebst