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We study the realizations of topological defects in 1d quantum Ising modelwith open boundary condition at criticality. Applying the constructiondiscussed in [M. Hauru, G. Evenbly, W. W. Ho, D. Gaiotto, and G. Vidal, Phys.Rev. B 94, 115125 (2016)], we prove that the Ising model on an open chain withmultiple topological defects can be transformed to the same model with boundarymagnetic fields and noninteracting boundary degrees of freedom. This results inthe appearance of linear combination of Cardy states [J. L. Cardy, Nucl. Phys.B 324, 581 (1989)], which can be interpreted as an edge state of the spin orfermion chain. We show that this edge state with the large boundary entropy canbe protected under bulk perturbation whereas it is fragile to a boundaryperturbation. Our formulation suggests an existence of nontrivial edge physicsunder the existence of topological defects and opens many interesting questionsfor future analysis related to boundary and bulk physics.

Open spin chain realization of topological defect on 1d Ising model and boundary and bulk symmetry