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Piercing The Rainbow State: Entanglement On An Inhomogeneous Spin Chain With A Defect

Physical review(2020)

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摘要
The rainbow state denotes a set of valence bond states organized concentrically around the center of a spin 1/2 chain. It is the ground state of an inhomogeneous XX Hamiltonian and presents a maximal violation of the area law of entanglement entropy. Here, we add a tunable exchange coupling constant at the center, gamma, and show that it induces entanglement transitions of the ground state. At very strong inhomogeneity, the rainbow state survives for 0 <= gamma <= 1, while outside that region the ground state is a product of dimers. In the weak inhomogeneity regime, the entanglement entropy satisfies a volume law, derived from CFT in curved space-time, with an effective central charge that depends on the inhomogeneity parameter and y. In all regimes we have found that the entanglement properties are invariant under the transformation gamma <-> 1 - gamma, whose fixed point gamma = 1/2 corresponds to the usual rainbow model. Finally, we study the robustness of nontrivial topological phases in the presence of the defect.
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关键词
inhomogeneous spin chain,entanglement,rainbow state
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