Twisted Quantum Double Model of Topological Orders with Boundaries

admin   2020-01-06 18:40:32   2734

报告题目:Twisted Quantum Double Model of Topological Orders with Boundaries
报告时间:2020-01-07 09:30 (星期二)
报告人:万义顿教授( 复旦大学)


We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group G and a 3-cocycle in the third cohomology group of G over U (1), a boundary Hamiltonian can be defined by a subgroup K of G and a 2-cochain in the second cochain group of K over U (1). The consistency between the bulk and boundary Hamiltonians is dictated by what we call the Frobenius condition that constrains the 2-cochain given the 3-cocyle. We offer a closed-form formula computing the ground-state degeneracy of the model on a cylinder in terms of the input data only, which can be naturally generalized to surfaces with more boundaries. We also explicitly write down the ground-state wave function of the model on a disk also in terms of the input data only. 



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