Open spin chain realization of a topological defect in a one-dimensional Ising model: Boundary and bulk symmetry

Abstract

We study the realizations of topological defects in a one-dimensional quantum Ising model with an open boundary condition at criticality. Applying the construction discussed 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 with multiple topological defects can be transformed to the same model with boundary magnetic fields and noninteracting boundary degrees of freedom. This results in the appearance of a linear combination of Cardy states, which can be interpreted as an edge state of the spin or fermion chain. We show that this edge state with the large boundary entropy can be protected under bulk perturbation, whereas it is fragile to a boundary perturbation. Our formulation suggests the existence of nontrivial edge physics under the existence of topological defects and opens many interesting questions for future analysis related to boundary and bulk physics.